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A264911 Number of 6-ascent sequences of length n with no consecutive repeated letters.

%I A264911 #12 Nov 09 2017 11:38:55
%S A264911 1,1,6,42,315,2541,21931,201761,1971627,20401115,222886237,2564378397,
%T A264911 30996823039,392772620555,5206946927601,72084153595073,
%U A264911 1040323636265431,15627180533214417,243970019981427565,3953119943277152705,66394925299770846495,1154518082416143179150
%N A264911 Number of 6-ascent sequences of length n with no consecutive repeated letters.
%H A264911 Alois P. Heinz, <a href="/A264911/b264911.txt">Table of n, a(n) for n = 0..200</a>
%H A264911 S. Kitaev, J. Remmel, <a href="https://arxiv.org/abs/1503.00914">p-Ascent Sequences</a>, arXiv:1503.00914 [math.CO], 2015.
%p A264911 b:= proc(n, i, t) option remember; `if`(n<1, 1, add(
%p A264911       `if`(j=i, 0, b(n-1, j, t+`if`(j>i, 1, 0))), j=0..t+6))
%p A264911     end:
%p A264911 a:= n-> (b(n-1, 0$2)):
%p A264911 seq(a(n), n=0..30);
%t A264911 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 + 6}]]; a[n_] := b[n - 1, 0, 0];
%t A264911 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Nov 09 2017, after _Alois P. Heinz_ *)
%Y A264911 Column k=6 of A264909.
%K A264911 nonn
%O A264911 0,3
%A A264911 _Alois P. Heinz_, Nov 28 2015