Integer classes for sums up to 1 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ] } }, "lists": { "1": [], "2": [ 0 ] } } } Integer classes for sums up to 2 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] } }, "lists": { "1": [], "2": [ 0, 1 ] } } } Integer classes for sums up to 3 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] }, "3": { "1,2": [ 2 ], "1,1,1": [ 3 ] } }, "lists": { "1": [], "2": [ 0, 1 ], "3": [ 2, 3 ] } } } Integer classes for sums up to 4 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] }, "3": { "1,2": [ 2 ], "1,1,1": [ 3 ] }, "4": { "1,3": [ 4 ], "1,1,2": [ 5, 6 ], "1,1,1,1": [ 7 ] } }, "lists": { "1": [], "2": [ 0, 1 ], "3": [ 2, 3 ], "4": [ 4, 5, 6, 7 ] } } } Integer classes for sums up to 5 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] }, "3": { "1,2": [ 2 ], "1,1,1": [ 3 ] }, "4": { "1,3": [ 4 ], "1,1,2": [ 5, 6 ], "1,1,1,1": [ 7 ] }, "5": { "1,4": [ 8 ], "1,1,3": [ 9, 12 ], "1,2,2": [ 10 ], "1,1,1,2": [ 11, 13, 14 ], "1,1,1,1,1": [ 15 ] } }, "lists": { "1": [], "2": [ 0, 1 ], "3": [ 2, 3 ], "4": [ 4, 5, 6, 7 ], "5": [ 8, 9, 10, 11, 12, 13, 14, 15 ] } } } Integer classes for sums up to 6 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] }, "3": { "1,2": [ 2 ], "1,1,1": [ 3 ] }, "4": { "1,3": [ 4 ], "1,1,2": [ 5, 6 ], "1,1,1,1": [ 7 ] }, "5": { "1,4": [ 8 ], "1,1,3": [ 9, 12 ], "1,2,2": [ 10 ], "1,1,1,2": [ 11, 13, 14 ], "1,1,1,1,1": [ 15 ] }, "6": { "1,5": [ 16 ], "1,1,4": [ 17, 24 ], "1,2,3": [ 18, 20 ], "1,1,1,3": [ 19, 25, 28 ], "1,1,2,2": [ 21, 22, 26 ], "1,1,1,1,2": [ 23, 27, 29, 30 ], "1,1,1,1,1,1": [ 31 ] } }, "lists": { "1": [], "2": [ 0, 1 ], "3": [ 2, 3 ], "4": [ 4, 5, 6, 7 ], "5": [ 8, 9, 10, 11, 12, 13, 14, 15 ], "6": [ 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ] } } } Integer classes for sums up to 7 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] }, "3": { "1,2": [ 2 ], "1,1,1": [ 3 ] }, "4": { "1,3": [ 4 ], "1,1,2": [ 5, 6 ], "1,1,1,1": [ 7 ] }, "5": { "1,4": [ 8 ], "1,1,3": [ 9, 12 ], "1,2,2": [ 10 ], "1,1,1,2": [ 11, 13, 14 ], "1,1,1,1,1": [ 15 ] }, "6": { "1,5": [ 16 ], "1,1,4": [ 17, 24 ], "1,2,3": [ 18, 20 ], "1,1,1,3": [ 19, 25, 28 ], "1,1,2,2": [ 21, 22, 26 ], "1,1,1,1,2": [ 23, 27, 29, 30 ], "1,1,1,1,1,1": [ 31 ] }, "7": { "1,6": [ 32 ], "1,1,5": [ 33, 48 ], "1,2,4": [ 34, 40 ], "1,1,1,4": [ 35, 49, 56 ], "1,3,3": [ 36 ], "1,1,2,3": [ 37, 38, 41, 44, 50, 52 ], "1,1,1,1,3": [ 39, 51, 57, 60 ], "1,2,2,2": [ 42 ], "1,1,1,2,2": [ 43, 45, 46, 53, 54, 58 ], "1,1,1,1,1,2": [ 47, 55, 59, 61, 62 ], "1,1,1,1,1,1,1": [ 63 ] } }, "lists": { "1": [], "2": [ 0, 1 ], "3": [ 2, 3 ], "4": [ 4, 5, 6, 7 ], "5": [ 8, 9, 10, 11, 12, 13, 14, 15 ], "6": [ 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ], "7": [ 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63 ] } } } Integer classes for sums up to 8 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] }, "3": { "1,2": [ 2 ], "1,1,1": [ 3 ] }, "4": { "1,3": [ 4 ], "1,1,2": [ 5, 6 ], "1,1,1,1": [ 7 ] }, "5": { "1,4": [ 8 ], "1,1,3": [ 9, 12 ], "1,2,2": [ 10 ], "1,1,1,2": [ 11, 13, 14 ], "1,1,1,1,1": [ 15 ] }, "6": { "1,5": [ 16 ], "1,1,4": [ 17, 24 ], "1,2,3": [ 18, 20 ], "1,1,1,3": [ 19, 25, 28 ], "1,1,2,2": [ 21, 22, 26 ], "1,1,1,1,2": [ 23, 27, 29, 30 ], "1,1,1,1,1,1": [ 31 ] }, "7": { "1,6": [ 32 ], "1,1,5": [ 33, 48 ], "1,2,4": [ 34, 40 ], "1,1,1,4": [ 35, 49, 56 ], "1,3,3": [ 36 ], "1,1,2,3": [ 37, 38, 41, 44, 50, 52 ], "1,1,1,1,3": [ 39, 51, 57, 60 ], "1,2,2,2": [ 42 ], "1,1,1,2,2": [ 43, 45, 46, 53, 54, 58 ], "1,1,1,1,1,2": [ 47, 55, 59, 61, 62 ], "1,1,1,1,1,1,1": [ 63 ] }, "8": { "1,7": [ 64 ], "1,1,6": [ 65, 96 ], "1,2,5": [ 66, 80 ], "1,1,1,5": [ 67, 97, 112 ], "1,3,4": [ 68, 72 ], "1,1,2,4": [ 69, 70, 81, 88, 98, 104 ], "1,1,1,1,4": [ 71, 99, 113, 120 ], "1,1,3,3": [ 73, 76, 100 ], "1,2,2,3": [ 74, 82, 84 ], "1,1,1,2,3": [ 75, 77, 78, 83, 89, 92, 101, 102, 105, 108, 114, 116 ], "1,1,1,1,1,3": [ 79, 103, 115, 121, 124 ], "1,1,2,2,2": [ 85, 86, 90, 106 ], "1,1,1,1,2,2": [ 87, 91, 93, 94, 107, 109, 110, 117, 118, 122 ], "1,1,1,1,1,1,2": [ 95, 111, 119, 123, 125, 126 ], "1,1,1,1,1,1,1,1": [ 127 ] } }, "lists": { "1": [], "2": [ 0, 1 ], "3": [ 2, 3 ], "4": [ 4, 5, 6, 7 ], "5": [ 8, 9, 10, 11, 12, 13, 14, 15 ], "6": [ 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ], "7": [ 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63 ], "8": [ 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127 ] } } } Integer classes for sums up to 9 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] }, "3": { "1,2": [ 2 ], "1,1,1": [ 3 ] }, "4": { "1,3": [ 4 ], "1,1,2": [ 5, 6 ], "1,1,1,1": [ 7 ] }, "5": { "1,4": [ 8 ], "1,1,3": [ 9, 12 ], "1,2,2": [ 10 ], "1,1,1,2": [ 11, 13, 14 ], "1,1,1,1,1": [ 15 ] }, "6": { "1,5": [ 16 ], "1,1,4": [ 17, 24 ], "1,2,3": [ 18, 20 ], "1,1,1,3": [ 19, 25, 28 ], "1,1,2,2": [ 21, 22, 26 ], "1,1,1,1,2": [ 23, 27, 29, 30 ], "1,1,1,1,1,1": [ 31 ] }, "7": { "1,6": [ 32 ], "1,1,5": [ 33, 48 ], "1,2,4": [ 34, 40 ], "1,1,1,4": [ 35, 49, 56 ], "1,3,3": [ 36 ], "1,1,2,3": [ 37, 38, 41, 44, 50, 52 ], "1,1,1,1,3": [ 39, 51, 57, 60 ], "1,2,2,2": [ 42 ], "1,1,1,2,2": [ 43, 45, 46, 53, 54, 58 ], "1,1,1,1,1,2": [ 47, 55, 59, 61, 62 ], "1,1,1,1,1,1,1": [ 63 ] }, "8": { "1,7": [ 64 ], "1,1,6": [ 65, 96 ], "1,2,5": [ 66, 80 ], "1,1,1,5": [ 67, 97, 112 ], "1,3,4": [ 68, 72 ], "1,1,2,4": [ 69, 70, 81, 88, 98, 104 ], "1,1,1,1,4": [ 71, 99, 113, 120 ], "1,1,3,3": [ 73, 76, 100 ], "1,2,2,3": [ 74, 82, 84 ], "1,1,1,2,3": [ 75, 77, 78, 83, 89, 92, 101, 102, 105, 108, 114, 116 ], "1,1,1,1,1,3": [ 79, 103, 115, 121, 124 ], "1,1,2,2,2": [ 85, 86, 90, 106 ], "1,1,1,1,2,2": [ 87, 91, 93, 94, 107, 109, 110, 117, 118, 122 ], "1,1,1,1,1,1,2": [ 95, 111, 119, 123, 125, 126 ], "1,1,1,1,1,1,1,1": [ 127 ] }, "9": { "1,8": [ 128 ], "1,1,7": [ 129, 192 ], "1,2,6": [ 130, 160 ], "1,1,1,6": [ 131, 193, 224 ], "1,3,5": [ 132, 144 ], "1,1,2,5": [ 133, 134, 161, 176, 194, 208 ], "1,1,1,1,5": [ 135, 195, 225, 240 ], "1,4,4": [ 136 ], "1,1,3,4": [ 137, 140, 145, 152, 196, 200 ], "1,2,2,4": [ 138, 162, 168 ], "1,1,1,2,4": [ 139, 141, 142, 163, 177, 184, 197, 198, 209, 216, 226, 232 ], "1,1,1,1,1,4": [ 143, 199, 227, 241, 248 ], "1,2,3,3": [ 146, 148, 164 ], "1,1,1,3,3": [ 147, 153, 156, 201, 204, 228 ], "1,1,2,2,3": [ 149, 150, 154, 165, 166, 169, 172, 178, 180, 202, 210, 212 ], "1,1,1,1,2,3": [ 151, 155, 157, 158, 167, 179, 185, 188, 203, 205, 206, 211, 217, 220, 229, 230, 233, 236, 242, 244 ], "1,1,1,1,1,1,3": [ 159, 207, 231, 243, 249, 252 ], "1,2,2,2,2": [ 170 ], "1,1,1,2,2,2": [ 171, 173, 174, 181, 182, 186, 213, 214, 218, 234 ], "1,1,1,1,1,2,2": [ 175, 183, 187, 189, 190, 215, 219, 221, 222, 235, 237, 238, 245, 246, 250 ], "1,1,1,1,1,1,1,2": [ 191, 223, 239, 247, 251, 253, 254 ], "1,1,1,1,1,1,1,1,1": [ 255 ] } }, "lists": { "1": [], "2": [ 0, 1 ], "3": [ 2, 3 ], "4": [ 4, 5, 6, 7 ], "5": [ 8, 9, 10, 11, 12, 13, 14, 15 ], "6": [ 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ], "7": [ 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63 ], "8": [ 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127 ], "9": [ 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255 ] } } } Integer classes for sums up to 10 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] }, "3": { "1,2": [ 2 ], "1,1,1": [ 3 ] }, "4": { "1,3": [ 4 ], "1,1,2": [ 5, 6 ], "1,1,1,1": [ 7 ] }, "5": { "1,4": [ 8 ], "1,1,3": [ 9, 12 ], "1,2,2": [ 10 ], "1,1,1,2": [ 11, 13, 14 ], "1,1,1,1,1": [ 15 ] }, "6": { "1,5": [ 16 ], "1,1,4": [ 17, 24 ], "1,2,3": [ 18, 20 ], "1,1,1,3": [ 19, 25, 28 ], "1,1,2,2": [ 21, 22, 26 ], "1,1,1,1,2": [ 23, 27, 29, 30 ], "1,1,1,1,1,1": [ 31 ] }, "7": { "1,6": [ 32 ], "1,1,5": [ 33, 48 ], "1,2,4": [ 34, 40 ], "1,1,1,4": [ 35, 49, 56 ], "1,3,3": [ 36 ], "1,1,2,3": [ 37, 38, 41, 44, 50, 52 ], "1,1,1,1,3": [ 39, 51, 57, 60 ], "1,2,2,2": [ 42 ], "1,1,1,2,2": [ 43, 45, 46, 53, 54, 58 ], "1,1,1,1,1,2": [ 47, 55, 59, 61, 62 ], "1,1,1,1,1,1,1": [ 63 ] }, "8": { "1,7": [ 64 ], "1,1,6": [ 65, 96 ], "1,2,5": [ 66, 80 ], "1,1,1,5": [ 67, 97, 112 ], "1,3,4": [ 68, 72 ], "1,1,2,4": [ 69, 70, 81, 88, 98, 104 ], "1,1,1,1,4": [ 71, 99, 113, 120 ], "1,1,3,3": [ 73, 76, 100 ], "1,2,2,3": [ 74, 82, 84 ], "1,1,1,2,3": [ 75, 77, 78, 83, 89, 92, 101, 102, 105, 108, 114, 116 ], "1,1,1,1,1,3": [ 79, 103, 115, 121, 124 ], "1,1,2,2,2": [ 85, 86, 90, 106 ], "1,1,1,1,2,2": [ 87, 91, 93, 94, 107, 109, 110, 117, 118, 122 ], "1,1,1,1,1,1,2": [ 95, 111, 119, 123, 125, 126 ], "1,1,1,1,1,1,1,1": [ 127 ] }, "9": { "1,8": [ 128 ], "1,1,7": [ 129, 192 ], "1,2,6": [ 130, 160 ], "1,1,1,6": [ 131, 193, 224 ], "1,3,5": [ 132, 144 ], "1,1,2,5": [ 133, 134, 161, 176, 194, 208 ], "1,1,1,1,5": [ 135, 195, 225, 240 ], "1,4,4": [ 136 ], "1,1,3,4": [ 137, 140, 145, 152, 196, 200 ], "1,2,2,4": [ 138, 162, 168 ], "1,1,1,2,4": [ 139, 141, 142, 163, 177, 184, 197, 198, 209, 216, 226, 232 ], "1,1,1,1,1,4": [ 143, 199, 227, 241, 248 ], "1,2,3,3": [ 146, 148, 164 ], "1,1,1,3,3": [ 147, 153, 156, 201, 204, 228 ], "1,1,2,2,3": [ 149, 150, 154, 165, 166, 169, 172, 178, 180, 202, 210, 212 ], "1,1,1,1,2,3": [ 151, 155, 157, 158, 167, 179, 185, 188, 203, 205, 206, 211, 217, 220, 229, 230, 233, 236, 242, 244 ], "1,1,1,1,1,1,3": [ 159, 207, 231, 243, 249, 252 ], "1,2,2,2,2": [ 170 ], "1,1,1,2,2,2": [ 171, 173, 174, 181, 182, 186, 213, 214, 218, 234 ], "1,1,1,1,1,2,2": [ 175, 183, 187, 189, 190, 215, 219, 221, 222, 235, 237, 238, 245, 246, 250 ], "1,1,1,1,1,1,1,2": [ 191, 223, 239, 247, 251, 253, 254 ], "1,1,1,1,1,1,1,1,1": [ 255 ] }, "10": { "1,9": [ 256 ], "1,1,8": [ 257, 384 ], "1,2,7": [ 258, 320 ], "1,1,1,7": [ 259, 385, 448 ], "1,3,6": [ 260, 288 ], "1,1,2,6": [ 261, 262, 321, 352, 386, 416 ], "1,1,1,1,6": [ 263, 387, 449, 480 ], "1,4,5": [ 264, 272 ], "1,1,3,5": [ 265, 268, 289, 304, 388, 400 ], "1,2,2,5": [ 266, 322, 336 ], "1,1,1,2,5": [ 267, 269, 270, 323, 353, 368, 389, 390, 417, 432, 450, 464 ], "1,1,1,1,1,5": [ 271, 391, 451, 481, 496 ], "1,1,4,4": [ 273, 280, 392 ], "1,2,3,4": [ 274, 276, 290, 296, 324, 328 ], "1,1,1,3,4": [ 275, 281, 284, 291, 305, 312, 393, 396, 401, 408, 452, 456 ], "1,1,2,2,4": [ 277, 278, 282, 325, 326, 337, 344, 354, 360, 394, 418, 424 ], "1,1,1,1,2,4": [ 279, 283, 285, 286, 327, 355, 369, 376, 395, 397, 398, 419, 433, 440, 453, 454, 465, 472, 482, 488 ], "1,1,1,1,1,1,4": [ 287, 399, 455, 483, 497, 504 ], "1,3,3,3": [ 292 ], "1,1,2,3,3": [ 293, 294, 297, 300, 306, 308, 329, 332, 356, 402, 404, 420 ], "1,1,1,1,3,3": [ 295, 307, 313, 316, 403, 409, 412, 457, 460, 484 ], "1,2,2,2,3": [ 298, 330, 338, 340 ], "1,1,1,2,2,3": [ 299, 301, 302, 309, 310, 314, 331, 333, 334, 339, 345, 348, 357, 358, 361, 364, 370, 372, 405, 406, 410, 421, 422, 425, 428, 434, 436, 458, 466, 468 ], "1,1,1,1,1,2,3": [ 303, 311, 315, 317, 318, 335, 359, 371, 377, 380, 407, 411, 413, 414, 423, 435, 441, 444, 459, 461, 462, 467, 473, 476, 485, 486, 489, 492, 498, 500 ], "1,1,1,1,1,1,1,3": [ 319, 415, 463, 487, 499, 505, 508 ], "1,1,2,2,2,2": [ 341, 342, 346, 362, 426 ], "1,1,1,1,2,2,2": [ 343, 347, 349, 350, 363, 365, 366, 373, 374, 378, 427, 429, 430, 437, 438, 442, 469, 470, 474, 490 ], "1,1,1,1,1,1,2,2": [ 351, 367, 375, 379, 381, 382, 431, 439, 443, 445, 446, 471, 475, 477, 478, 491, 493, 494, 501, 502, 506 ], "1,1,1,1,1,1,1,1,2": [ 383, 447, 479, 495, 503, 507, 509, 510 ], "1,1,1,1,1,1,1,1,1,1": [ 511 ] } }, "lists": { "1": [], "2": [ 0, 1 ], "3": [ 2, 3 ], "4": [ 4, 5, 6, 7 ], "5": [ 8, 9, 10, 11, 12, 13, 14, 15 ], "6": [ 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ], "7": [ 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63 ], "8": [ 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127 ], "9": [ 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255 ], "10": [ 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511 ] } } } Integer classes for sums up to 11 { "sums": { "classes": { "1": { "1": [] }, "2": { "2": [ 0 ], "1,1": [ 1 ] }, "3": { "1,2": [ 2 ], "1,1,1": [ 3 ] }, "4": { "1,3": [ 4 ], "1,1,2": [ 5, 6 ], "1,1,1,1": [ 7 ] }, "5": { "1,4": [ 8 ], "1,1,3": [ 9, 12 ], "1,2,2": [ 10 ], "1,1,1,2": [ 11, 13, 14 ], "1,1,1,1,1": [ 15 ] }, "6": { "1,5": [ 16 ], "1,1,4": [ 17, 24 ], "1,2,3": [ 18, 20 ], "1,1,1,3": [ 19, 25, 28 ], "1,1,2,2": [ 21, 22, 26 ], "1,1,1,1,2": [ 23, 27, 29, 30 ], "1,1,1,1,1,1": [ 31 ] }, "7": { "1,6": [ 32 ], "1,1,5": [ 33, 48 ], "1,2,4": [ 34, 40 ], "1,1,1,4": [ 35, 49, 56 ], "1,3,3": [ 36 ], "1,1,2,3": [ 37, 38, 41, 44, 50, 52 ], "1,1,1,1,3": [ 39, 51, 57, 60 ], "1,2,2,2": [ 42 ], "1,1,1,2,2": [ 43, 45, 46, 53, 54, 58 ], "1,1,1,1,1,2": [ 47, 55, 59, 61, 62 ], "1,1,1,1,1,1,1": [ 63 ] }, "8": { "1,7": [ 64 ], "1,1,6": [ 65, 96 ], "1,2,5": [ 66, 80 ], "1,1,1,5": [ 67, 97, 112 ], "1,3,4": [ 68, 72 ], "1,1,2,4": [ 69, 70, 81, 88, 98, 104 ], "1,1,1,1,4": [ 71, 99, 113, 120 ], "1,1,3,3": [ 73, 76, 100 ], "1,2,2,3": [ 74, 82, 84 ], "1,1,1,2,3": [ 75, 77, 78, 83, 89, 92, 101, 102, 105, 108, 114, 116 ], "1,1,1,1,1,3": [ 79, 103, 115, 121, 124 ], "1,1,2,2,2": [ 85, 86, 90, 106 ], "1,1,1,1,2,2": [ 87, 91, 93, 94, 107, 109, 110, 117, 118, 122 ], "1,1,1,1,1,1,2": [ 95, 111, 119, 123, 125, 126 ], "1,1,1,1,1,1,1,1": [ 127 ] }, "9": { "1,8": [ 128 ], "1,1,7": [ 129, 192 ], "1,2,6": [ 130, 160 ], "1,1,1,6": [ 131, 193, 224 ], "1,3,5": [ 132, 144 ], "1,1,2,5": [ 133, 134, 161, 176, 194, 208 ], "1,1,1,1,5": [ 135, 195, 225, 240 ], "1,4,4": [ 136 ], "1,1,3,4": [ 137, 140, 145, 152, 196, 200 ], "1,2,2,4": [ 138, 162, 168 ], "1,1,1,2,4": [ 139, 141, 142, 163, 177, 184, 197, 198, 209, 216, 226, 232 ], "1,1,1,1,1,4": [ 143, 199, 227, 241, 248 ], "1,2,3,3": [ 146, 148, 164 ], "1,1,1,3,3": [ 147, 153, 156, 201, 204, 228 ], "1,1,2,2,3": [ 149, 150, 154, 165, 166, 169, 172, 178, 180, 202, 210, 212 ], "1,1,1,1,2,3": [ 151, 155, 157, 158, 167, 179, 185, 188, 203, 205, 206, 211, 217, 220, 229, 230, 233, 236, 242, 244 ], "1,1,1,1,1,1,3": [ 159, 207, 231, 243, 249, 252 ], "1,2,2,2,2": [ 170 ], "1,1,1,2,2,2": [ 171, 173, 174, 181, 182, 186, 213, 214, 218, 234 ], "1,1,1,1,1,2,2": [ 175, 183, 187, 189, 190, 215, 219, 221, 222, 235, 237, 238, 245, 246, 250 ], "1,1,1,1,1,1,1,2": [ 191, 223, 239, 247, 251, 253, 254 ], "1,1,1,1,1,1,1,1,1": [ 255 ] }, "10": { "1,9": [ 256 ], "1,1,8": [ 257, 384 ], "1,2,7": [ 258, 320 ], "1,1,1,7": [ 259, 385, 448 ], "1,3,6": [ 260, 288 ], "1,1,2,6": [ 261, 262, 321, 352, 386, 416 ], "1,1,1,1,6": [ 263, 387, 449, 480 ], "1,4,5": [ 264, 272 ], "1,1,3,5": [ 265, 268, 289, 304, 388, 400 ], "1,2,2,5": [ 266, 322, 336 ], "1,1,1,2,5": [ 267, 269, 270, 323, 353, 368, 389, 390, 417, 432, 450, 464 ], "1,1,1,1,1,5": [ 271, 391, 451, 481, 496 ], "1,1,4,4": [ 273, 280, 392 ], "1,2,3,4": [ 274, 276, 290, 296, 324, 328 ], "1,1,1,3,4": [ 275, 281, 284, 291, 305, 312, 393, 396, 401, 408, 452, 456 ], "1,1,2,2,4": [ 277, 278, 282, 325, 326, 337, 344, 354, 360, 394, 418, 424 ], "1,1,1,1,2,4": [ 279, 283, 285, 286, 327, 355, 369, 376, 395, 397, 398, 419, 433, 440, 453, 454, 465, 472, 482, 488 ], "1,1,1,1,1,1,4": [ 287, 399, 455, 483, 497, 504 ], "1,3,3,3": [ 292 ], "1,1,2,3,3": [ 293, 294, 297, 300, 306, 308, 329, 332, 356, 402, 404, 420 ], "1,1,1,1,3,3": [ 295, 307, 313, 316, 403, 409, 412, 457, 460, 484 ], "1,2,2,2,3": [ 298, 330, 338, 340 ], "1,1,1,2,2,3": [ 299, 301, 302, 309, 310, 314, 331, 333, 334, 339, 345, 348, 357, 358, 361, 364, 370, 372, 405, 406, 410, 421, 422, 425, 428, 434, 436, 458, 466, 468 ], "1,1,1,1,1,2,3": [ 303, 311, 315, 317, 318, 335, 359, 371, 377, 380, 407, 411, 413, 414, 423, 435, 441, 444, 459, 461, 462, 467, 473, 476, 485, 486, 489, 492, 498, 500 ], "1,1,1,1,1,1,1,3": [ 319, 415, 463, 487, 499, 505, 508 ], "1,1,2,2,2,2": [ 341, 342, 346, 362, 426 ], "1,1,1,1,2,2,2": [ 343, 347, 349, 350, 363, 365, 366, 373, 374, 378, 427, 429, 430, 437, 438, 442, 469, 470, 474, 490 ], "1,1,1,1,1,1,2,2": [ 351, 367, 375, 379, 381, 382, 431, 439, 443, 445, 446, 471, 475, 477, 478, 491, 493, 494, 501, 502, 506 ], "1,1,1,1,1,1,1,1,2": [ 383, 447, 479, 495, 503, 507, 509, 510 ], "1,1,1,1,1,1,1,1,1,1": [ 511 ] }, "11": { "1,10": [ 512 ], "1,1,9": [ 513, 768 ], "1,2,8": [ 514, 640 ], "1,1,1,8": [ 515, 769, 896 ], "1,3,7": [ 516, 576 ], "1,1,2,7": [ 517, 518, 641, 704, 770, 832 ], "1,1,1,1,7": [ 519, 771, 897, 960 ], "1,4,6": [ 520, 544 ], "1,1,3,6": [ 521, 524, 577, 608, 772, 800 ], "1,2,2,6": [ 522, 642, 672 ], "1,1,1,2,6": [ 523, 525, 526, 643, 705, 736, 773, 774, 833, 864, 898, 928 ], "1,1,1,1,1,6": [ 527, 775, 899, 961, 992 ], "1,5,5": [ 528 ], "1,1,4,5": [ 529, 536, 545, 560, 776, 784 ], "1,2,3,5": [ 530, 532, 578, 592, 644, 656 ], "1,1,1,3,5": [ 531, 537, 540, 579, 609, 624, 777, 780, 801, 816, 900, 912 ], "1,1,2,2,5": [ 533, 534, 538, 645, 646, 673, 688, 706, 720, 778, 834, 848 ], "1,1,1,1,2,5": [ 535, 539, 541, 542, 647, 707, 737, 752, 779, 781, 782, 835, 865, 880, 901, 902, 929, 944, 962, 976 ], "1,1,1,1,1,1,5": [ 543, 783, 903, 963, 993, 1008 ], "1,2,4,4": [ 546, 552, 648 ], "1,1,1,4,4": [ 547, 561, 568, 785, 792, 904 ], "1,3,3,4": [ 548, 580, 584 ], "1,1,2,3,4": [ 549, 550, 553, 556, 562, 564, 581, 582, 593, 600, 610, 616, 649, 652, 657, 664, 708, 712, 786, 788, 802, 808, 836, 840 ], "1,1,1,1,3,4": [ 551, 563, 569, 572, 583, 611, 625, 632, 787, 793, 796, 803, 817, 824, 905, 908, 913, 920, 964, 968 ], "1,2,2,2,4": [ 554, 650, 674, 680 ], "1,1,1,2,2,4": [ 555, 557, 558, 565, 566, 570, 651, 653, 654, 675, 689, 696, 709, 710, 721, 728, 738, 744, 789, 790, 794, 837, 838, 849, 856, 866, 872, 906, 930, 936 ], "1,1,1,1,1,2,4": [ 559, 567, 571, 573, 574, 655, 711, 739, 753, 760, 791, 795, 797, 798, 839, 867, 881, 888, 907, 909, 910, 931, 945, 952, 965, 966, 977, 984, 994, 1000 ], "1,1,1,1,1,1,1,4": [ 575, 799, 911, 967, 995, 1009, 1016 ], "1,1,3,3,3": [ 585, 588, 612, 804 ], "1,2,2,3,3": [ 586, 594, 596, 658, 660, 676 ], "1,1,1,2,3,3": [ 587, 589, 590, 595, 601, 604, 613, 614, 617, 620, 626, 628, 659, 665, 668, 713, 716, 740, 805, 806, 809, 812, 818, 820, 841, 844, 868, 914, 916, 932 ], "1,1,1,1,1,3,3": [ 591, 615, 627, 633, 636, 807, 819, 825, 828, 915, 921, 924, 969, 972, 996 ], "1,1,2,2,2,3": [ 597, 598, 602, 618, 661, 662, 666, 677, 678, 681, 684, 690, 692, 714, 722, 724, 810, 842, 850, 852 ], "1,1,1,1,2,2,3": [ 599, 603, 605, 606, 619, 621, 622, 629, 630, 634, 663, 667, 669, 670, 679, 691, 697, 700, 715, 717, 718, 723, 729, 732, 741, 742, 745, 748, 754, 756, 811, 813, 814, 821, 822, 826, 843, 845, 846, 851, 857, 860, 869, 870, 873, 876, 882, 884, 917, 918, 922, 933, 934, 937, 940, 946, 948, 970, 978, 980 ], "1,1,1,1,1,1,2,3": [ 607, 623, 631, 635, 637, 638, 671, 719, 743, 755, 761, 764, 815, 823, 827, 829, 830, 847, 871, 883, 889, 892, 919, 923, 925, 926, 935, 947, 953, 956, 971, 973, 974, 979, 985, 988, 997, 998, 1001, 1004, 1010, 1012 ], "1,1,1,1,1,1,1,1,3": [ 639, 831, 927, 975, 999, 1011, 1017, 1020 ], "1,2,2,2,2,2": [ 682 ], "1,1,1,2,2,2,2": [ 683, 685, 686, 693, 694, 698, 725, 726, 730, 746, 853, 854, 858, 874, 938 ], "1,1,1,1,1,2,2,2": [ 687, 695, 699, 701, 702, 727, 731, 733, 734, 747, 749, 750, 757, 758, 762, 855, 859, 861, 862, 875, 877, 878, 885, 886, 890, 939, 941, 942, 949, 950, 954, 981, 982, 986, 1002 ], "1,1,1,1,1,1,1,2,2": [ 703, 735, 751, 759, 763, 765, 766, 863, 879, 887, 891, 893, 894, 943, 951, 955, 957, 958, 983, 987, 989, 990, 1003, 1005, 1006, 1013, 1014, 1018 ], "1,1,1,1,1,1,1,1,1,2": [ 767, 895, 959, 991, 1007, 1015, 1019, 1021, 1022 ], "1,1,1,1,1,1,1,1,1,1,1": [ 1023 ] } }, "lists": { "1": [], "2": [ 0, 1 ], "3": [ 2, 3 ], "4": [ 4, 5, 6, 7 ], "5": [ 8, 9, 10, 11, 12, 13, 14, 15 ], "6": [ 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ], "7": [ 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63 ], "8": [ 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127 ], "9": [ 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255 ], "10": [ 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511 ], "11": [ 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 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817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023 ] } } }