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%I #17 Apr 16 2021 00:16:11
%S 1,1,1,5,0,1,20,3,0,1,102,14,3,0,1,627,72,17,3,0,1,4461,468,87,20,3,0,
%T 1,36155,3453,582,103,23,3,0,1,328849,28782,4395,704,120,26,3,0,1,
%U 3317272,267831,37257,5435,834,138,29,3,0,1
%N Triangle read by rows: number of circular permutations of [1..n] with k progressions of rise 1, distance 1 and length 3 (n >= 3, k >= 0).
%D Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012.
%e Triangle begins:
%e 1;
%e 1, 1; [this is row n=3]
%e 5, 0, 1;
%e 20, 3, 0, 1;
%e 102, 14, 3, 0, 1;
%e 627, 72, 17, 3, 0, 1;
%e 4461, 468, 87, 20, 3, 0, 1;
%e 36155, 3453, 582, 103, 23, 3, 0, 1;
%e 328849, 28782, 4395, 704, 120, 26, 3, 0, 1;
%e 3317272, 267831, 37257, 5435, 834, 138, 29, 3, 0, 1;
%e ...
%Y Cf. A216716, A174072, A165961, A180187.
%K nonn,tabl
%O 2,4
%A _N. J. A. Sloane_, Sep 15 2012
%E a(2,0)=1 added by _N. J. A. Sloane_, Apr 16 2021
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