login
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).
6

%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