cp's OEIS Frontend

A369326 Array read by ascending antidiagonals: A(n,k) is the number of words of length n over the alphabet [k] and sortable by a (2,1)-pop stack of depth 2.

%I A369326 #14 Jan 22 2024 00:03:07
%S A369326 1,0,1,0,1,1,0,1,2,1,0,1,4,3,1,0,1,8,9,4,1,0,1,16,24,16,5,1,0,1,32,59,
%T A369326 52,25,6,1,0,1,64,138,149,95,36,7,1,0,1,128,313,396,310,156,49,8,1,0,
%U A369326 1,256,696,1003,923,571,238,64,9,1,0,1,512,1527,2458,2585,1884,966,344,81,10,1
%N A369326 Array read by ascending antidiagonals: A(n,k) is the number of words of length n over the alphabet [k] and sortable by a (2,1)-pop stack of depth 2.
%H A369326 Toufik Mansour, Howard Skogman, and Rebecca Smith, <a href="https://arxiv.org/abs/2401.06662">Sorting inversion sequences</a>, arXiv:2401.06662 [math.CO], 2024. See Theorem 3.25 at page 13.
%F A369326 G.f.: ((1 - x)(1 - 2*x) - ((1 - x)*(1 - 2*x) + x^2)*y)/((1 - x)*(1 - 2*x) - (1 - x)*(2 - 3*x)*y + (1 - 2*x)*y^2).
%e A369326 The array begins:
%e A369326   1, 1,  1,   1,   1,   1, ...
%e A369326   0, 1,  2,   3,   4,   5, ...
%e A369326   0, 1,  4,   9,  16,  25, ...
%e A369326   0, 1,  8,  24,  52,  95, ...
%e A369326   0, 1, 16,  59, 149, 310, ...
%e A369326   0, 1, 32, 138, 396, 923, ...
%e A369326   ...
%t A369326 A[n_,k_]:=SeriesCoefficient[((1-x)(1-2x)-((1-x)(1-2x)+x^2)y)/((1-x)(1-2x)-(1-x)(2-3x)y+(1-2x)y^2),{x,0,n},{y,0,k}]; Table[A[n-k,k],{n,0,11},{k,0,n}]//Flatten
%Y A369326 Cf. A000007 (k=0), A000012 (k=1 or n=0), A000079 (k=2).
%Y A369326 Cf. A001477 (n=1), A000290 (n=2), A256857 (n=3).
%Y A369326 Cf. A369324, A369327 (main diagonal), A369328 (antidiagonal sums).
%K A369326 nonn,tabl
%O A369326 0,9
%A A369326 _Stefano Spezia_, Jan 20 2024