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A263852 Number of 2-ascent sequences of length n with no consecutive repeated letters.

%I A263852 #20 Feb 17 2016 11:35:42
%S A263852 1,1,2,6,21,87,413,2213,13205,86828,623712,4859307,40810353,367525528,
%T A263852 3532986232,36107260781,390938180027,4470065574970,53825174198772,
%U A263852 680796406765054,9024180239004754,125096535241364056,1810074349321324370,27289548352480937756
%N A263852 Number of 2-ascent sequences of length n with no consecutive repeated letters.
%H A263852 Alois P. Heinz, <a href="/A263852/b263852.txt">Table of n, a(n) for n = 0..200</a>
%H A263852 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 A263852 b:= proc(n, i, t) option remember; `if`(n<1, 1, add(
%p A263852       `if`(j=i, 0, b(n-1, j, t+`if`(j>i, 1, 0))), j=0..t+2))
%p A263852     end:
%p A263852 a:= n-> b(n-1, 0$2):
%p A263852 seq(a(n), n=0..30);  # _Alois P. Heinz_, Nov 19 2015
%t A263852 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+2}]]; a[n_] := b[n-1, 0, 0]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Feb 17 2016, after _Alois P. Heinz_ *)
%Y A263852 Column k=2 of A264909.
%K A263852 nonn
%O A263852 0,3
%A A263852 _N. J. A. Sloane_, Nov 18 2015
%E A263852 a(10)-a(23) from _Alois P. Heinz_, Nov 19 2015