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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
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
1,3
COMMENTS
Asymptotics can be found in Goh and Zhao (2020). The column k=2 corresponds to the number of 3-free permutations of 1..n, for n>=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.
EXAMPLE
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
CROSSREFS
Cf. A003407 (column k=2), A338993, A339942.
Sequence in context: A144289 A293815 A373691 * A211318 A324239 A274706
KEYWORD
nonn,tabl
AUTHOR
Marcel K. Goh, Dec 23 2020
STATUS
approved