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

1, 1, 3, 12, 54, 276, 1574, 9916, 68394, 512671, 4150148, 36086135, 335447341, 3319876281, 34853551700, 386889999296, 4527701024471, 55715658165361, 719205555167707, 9717733698168073, 137168409543673446, 2018981393006166050, 30936712227446490134

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=3 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+3))
    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 + 3}]]; 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(22) from Alois P. Heinz, Nov 19 2015