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A264913 Number of 8-ascent sequences of length n with no consecutive repeated letters.

%I A264913 #12 Nov 09 2017 11:39:02
%S A264913 1,1,8,72,684,6876,72924,814056,9544164,117284766,1507813722,
%T A264913 20243939784,283383218358,4129738188546,62563457162916,
%U A264913 983985264479016,16046556350152008,271012423865891076,4735104984115971090,85496795448023574282,1593757450233067980306
%N A264913 Number of 8-ascent sequences of length n with no consecutive repeated letters.
%H A264913 Alois P. Heinz, <a href="/A264913/b264913.txt">Table of n, a(n) for n = 0..200</a>
%H A264913 S. Kitaev, J. Remmel, <a href="https://arxiv.org/abs/1503.00914">p-Ascent Sequences</a>, arXiv:1503.00914 [math.CO], 2015.
%p A264913 b:= proc(n, i, t) option remember; `if`(n<1, 1, add(
%p A264913       `if`(j=i, 0, b(n-1, j, t+`if`(j>i, 1, 0))), j=0..t+8))
%p A264913     end:
%p A264913 a:= n-> (b(n-1, 0$2)):
%p A264913 seq(a(n), n=0..30);
%t A264913 b[n_, i_, t_] := b[n, i, t] = If[n < 1, 1, Sum[If[j == i, 0, b[n - 1, j, t + If[j > i, 1, 0]]], {j, 0, t + 8}]]; a[n_] := b[n - 1, 0, 0];
%t A264913 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Nov 09 2017, after _Alois P. Heinz_ *)
%Y A264913 Column k=8 of A264909.
%K A264913 nonn
%O A264913 0,3
%A A264913 _Alois P. Heinz_, Nov 28 2015