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

1, 1, 2, 6, 21, 87, 413, 2213, 13205, 86828, 623712, 4859307, 40810353, 367525528, 3532986232, 36107260781, 390938180027, 4470065574970, 53825174198772, 680796406765054, 9024180239004754, 125096535241364056, 1810074349321324370, 27289548352480937756

Offset: 0

Author

N. J. A. Sloane, Nov 18 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• S. Kitaev, J. Remmel, p-Ascent Sequences, arXiv preprint arXiv:1503.00914 [math.CO], 2015.

Crossrefs

Column k=2 of A264909.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n<1, 1, add(
      `if`(j=i, 0, b(n-1, j, t+`if`(j>i, 1, 0))), j=0..t+2))
    end:
a:= n-> b(n-1, 0$2):
seq(a(n), n=0..30);  # Alois P. Heinz, Nov 19 2015

Mathematica

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 *)

Extensions

a(10)-a(23) from Alois P. Heinz, Nov 19 2015