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%I #14 Feb 01 2021 13:20:23
%S 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,
%T 198,24,2,0,282,21984,15702,2048,274,28,2,0,496,168368,162368,28048,
%U 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
%N Triangle read by rows: T(n,k) is the number of permutations of {1,...,n} whose longest embedded arithmetic progression has length k.
%C 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.
%H M. K. Goh and R. Y. Zhao, <a href="https://arxiv.org/abs/2012.12339">Arithmetic subsequences in a random ordering of an additive set</a>, arXiv:2012.12339 [math.CO], 2020.
%e Triangle T(n,k) begins:
%e n/k 1 2 3 4 5 6 7 8 9 10 11 12
%e 1 1
%e 2 0 2
%e 3 0 4 2
%e 4 0 10 12 2
%e 5 0 20 82 16 2
%e 6 0 48 516 134 20 2
%e 7 0 104 3232 1480 198 24 2
%e 8 0 282 21984 15702 2048 274 28 2
%e 9 0 496 168368 162368 28048 3204 362 32 2
%e 10 0 1066 1306404 1902496 374194 39420 4720 462 36 2
%e 11 0 2460 11064306 23226786 4929828 622140 64020 6644 574 40 2
%e 12 0 6128 101355594 298314654 68584052 9719492 913440 98472 9024 698 44 2
%Y Cf. A003407 (column k=2), A338993, A339942.
%K nonn,tabl
%O 1,3
%A _Marcel K. Goh_, Dec 23 2020
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