cp's OEIS Frontend

A216719 Triangle read by rows: number of circular permutations of [1..n] with k progressions of rise 1, distance 2 and length 3 (n >= 3, k >= 0).

%I A216719 #9 Apr 13 2021 19:21:24
%S A216719 2,6,22,2,109,10,1,657,55,7,1,4625,356,54,4,1,37186,2723,362,44,4,1,
%T A216719 336336,23300,2837,368,34,4,1,3379058,220997,25408,2967,330,35,4,1,
%U A216719 37328103,2308564,249736,26964,3100,292,36,4,1
%N A216719 Triangle read by rows: number of circular permutations of [1..n] with k progressions of rise 1, distance 2 and length 3 (n >= 3, k >= 0).
%D A216719 Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012.
%e A216719 Triangle begins:
%e A216719          2
%e A216719          6
%e A216719         22       2
%e A216719        109      10      1
%e A216719        657      55      7     1
%e A216719       4625     356     54     4    1
%e A216719      37186    2723    362    44    4   1
%e A216719     336336   23300   2837   368   34   4  1
%e A216719    3379058  220997  25408  2967  330  35  4 1
%e A216719   37328103 2308564 249736 26964 3100 292 36 4 1
%e A216719   ...
%Y A216719 Columns 1..2 are A174074, A216721.
%Y A216719 Row sums are A000142(n-1).
%Y A216719 Cf. A216716, A216718.
%K A216719 nonn,tabf
%O A216719 3,1
%A A216719 _N. J. A. Sloane_, Sep 15 2012