A339941 Triangle read by rows: T(n,k) is the number of permutations of {1,...,n} whose longest embedded arithmetic progression has length k.
1, 0, 2, 0, 4, 2, 0, 10, 12, 2, 0, 20, 82, 16, 2, 0, 48, 516, 134, 20, 2, 0, 104, 3232, 1480, 198, 24, 2, 0, 282, 21984, 15702, 2048, 274, 28, 2, 0, 496, 168368, 162368, 28048, 3204, 362, 32, 2, 0, 1066, 1306404, 1902496, 374194, 39420, 4720, 462, 36, 2, 0, 2460, 11064306, 23226786, 4929828, 622140, 64020, 6644, 574, 40, 2
Offset: 1
Examples
Triangle T(n,k) begins: n/k 1 2 3 4 5 6 7 8 9 10 11 12 1 1 2 0 2 3 0 4 2 4 0 10 12 2 5 0 20 82 16 2 6 0 48 516 134 20 2 7 0 104 3232 1480 198 24 2 8 0 282 21984 15702 2048 274 28 2 9 0 496 168368 162368 28048 3204 362 32 2 10 0 1066 1306404 1902496 374194 39420 4720 462 36 2 11 0 2460 11064306 23226786 4929828 622140 64020 6644 574 40 2 12 0 6128 101355594 298314654 68584052 9719492 913440 98472 9024 698 44 2
Links
- M. K. Goh and R. Y. Zhao, Arithmetic subsequences in a random ordering of an additive set, arXiv:2012.12339 [math.CO], 2020.
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