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

1, 1, 6, 42, 315, 2541, 21931, 201761, 1971627, 20401115, 222886237, 2564378397, 30996823039, 392772620555, 5206946927601, 72084153595073, 1040323636265431, 15627180533214417, 243970019981427565, 3953119943277152705, 66394925299770846495, 1154518082416143179150

Offset: 0

Author

Alois P. Heinz, Nov 28 2015

Keywords

• nonn

Links

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

Crossrefs

Column k=6 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+6))
    end:
a:= n-> (b(n-1, 0$2)):
seq(a(n), n=0..30);

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 + 6}]]; a[n_] := b[n - 1, 0, 0];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 09 2017, after Alois P. Heinz *)