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%I #16 Apr 14 2021 05:28:03
%S 1,0,0,1,5,0,0,0,1,18,5,0,0,0,1,95,18,6,0,0,0,1,600,84,28,7,0,0,0,1,
%T 4307,568,116,40,8,0,0,0,1,35168,4122,810,156,54,9,0,0,0,1,321609,
%U 33910,5975,1100,205,70,10,0,0,0,1
%N Triangle read by rows: number of circular permutations of [1..n] with k modular progressions of rise 1, distance 1 and length 3 (n >= 3, 0 <= k <= n).
%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, 0, 0, 1;
%e 5, 0, 0, 0, 1;
%e 18, 5, 0, 0, 0, 1;
%e 95, 18, 6, 0, 0, 0, 1;
%e 600, 84, 28, 7, 0, 0, 0, 1;
%e 4307, 568, 116, 40, 8, 0, 0, 0, 1;
%e 35168, 4122, 810, 156, 54, 9, 0, 0, 0, 1;
%e 321609, 33910, 5975, 1100, 205, 70, 10, 0, 0, 0, 1;
%e ...
%Y Columns 1..2 are A165962, A216723.
%Y Row sums are A000142(n-1).
%Y Cf. A216716, A216718, A216719, A165962.
%K nonn,tabf
%O 3,5
%A _N. J. A. Sloane_, Sep 15 2012
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