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A369325 a(n) is the number of words of length n over the alphabet [n], avoiding 120 and 210, and sortable by a stack of depth 2.

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%I A369325 #14 Jan 22 2024 00:02:50
%S A369325 0,1,4,25,176,1281,9472,70785,533248,4042753,30808064,235778049,
%T A369325 1810915328,13951401985,107765334016,834322202625,6472333459456,
%U A369325 50299072937985,391513776848896,3051764505903105,23818327111499776,186112536460918785,1455790849571946496,11398349517712523265
%N A369325 a(n) is the number of words of length n over the alphabet [n], avoiding 120 and 210, and sortable by a stack of depth 2.
%H A369325 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 3.18 at page 10.
%F A369325 a(n) = A000035(n) + 2^n*Sum_{i=0..floor((n-2)/2)} binomial(2*(n - i)- 3, n - 1).
%F A369325 a(n) ~ 8^(n-1)*hypergeom([1, 1 - n/2, (3 - n)/2], [(3 - 2*n)/2, 2 - n], 1)/sqrt(n*Pi).
%t A369325 a[n_] := (1-(-1)^n)/2 + 2^n*Sum[Binomial[2(n-i)-3,n-1],{i,0,Floor[(n-2)/2]}]; Array[a,24,0]
%Y A369325 Main diagonal of A369324.
%Y A369325 Cf. A000035, A369327.
%K A369325 nonn
%O A369325 0,3
%A A369325 _Stefano Spezia_, Jan 20 2024