cp's OEIS Frontend

A263853 Number of 3-ascent sequences of length n with no consecutive repeated letters.

%I A263853 #16 Feb 17 2016 10:26:26
%S A263853 1,1,3,12,54,276,1574,9916,68394,512671,4150148,36086135,335447341,
%T A263853 3319876281,34853551700,386889999296,4527701024471,55715658165361,
%U A263853 719205555167707,9717733698168073,137168409543673446,2018981393006166050,30936712227446490134
%N A263853 Number of 3-ascent sequences of length n with no consecutive repeated letters.
%H A263853 Alois P. Heinz, <a href="/A263853/b263853.txt">Table of n, a(n) for n = 0..200</a>
%H A263853 S. Kitaev, J. Remmel, <a href="http://arxiv.org/abs/1503.00914">p-Ascent Sequences</a>, arXiv preprint arXiv:1503.00914 [math.CO], 2015.
%p A263853 b:= proc(n, i, t) option remember; `if`(n<1, 1, add(
%p A263853       `if`(j=i, 0, b(n-1, j, t+`if`(j>i, 1, 0))), j=0..t+3))
%p A263853     end:
%p A263853 a:= n-> (b(n-1, 0$2)):
%p A263853 seq(a(n), n=0..30);  # _Alois P. Heinz_, Nov 19 2015
%t A263853 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 + 3}]]; a[n_] := b[n - 1, 0, 0]; Table[ a[n], {n, 0, 30}] (* _Jean-François Alcover_, Feb 17 2016, after _Alois P. Heinz_ *)
%Y A263853 Column k=3 of A264909.
%K A263853 nonn
%O A263853 0,3
%A A263853 _N. J. A. Sloane_, Nov 18 2015
%E A263853 a(10)-a(22) from _Alois P. Heinz_, Nov 19 2015