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A264910 Number of 5-ascent sequences of length n with no consecutive repeated letters.

%I A264910 #9 Aug 14 2017 03:31:54
%S A264910 1,1,5,30,195,1380,10555,86815,764350,7174420,71532369,755136887,
%T A264910 8415519048,98744576456,1216948265335,15718032335081,212330461568282,
%U A264910 2994374695258034,44008250794756373,672986694107199687,10692604102273015636,176266660430175342285
%N A264910 Number of 5-ascent sequences of length n with no consecutive repeated letters.
%H A264910 Alois P. Heinz, <a href="/A264910/b264910.txt">Table of n, a(n) for n = 0..200</a>
%H A264910 S. Kitaev, J. Remmel, <a href="https://arxiv.org/abs/1503.00914">p-Ascent Sequences</a>, arXiv:1503.00914 [math.CO], 2015
%p A264910 b:= proc(n, i, t) option remember; `if`(n<1, 1, add(
%p A264910       `if`(j=i, 0, b(n-1, j, t+`if`(j>i, 1, 0))), j=0..t+5))
%p A264910     end:
%p A264910 a:= n-> (b(n-1, 0$2)):
%p A264910 seq(a(n), n=0..30);
%t A264910 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+5}]];
%t A264910 a[n_] := b[n-1, 0, 0];
%t A264910 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Aug 14 2017, translated from Maple *)
%Y A264910 Column k=5 of A264909.
%K A264910 nonn
%O A264910 0,3
%A A264910 _Alois P. Heinz_, Nov 28 2015