A264913 Number of 8-ascent sequences of length n with no consecutive repeated letters.

1, 1, 8, 72, 684, 6876, 72924, 814056, 9544164, 117284766, 1507813722, 20243939784, 283383218358, 4129738188546, 62563457162916, 983985264479016, 16046556350152008, 271012423865891076, 4735104984115971090, 85496795448023574282, 1593757450233067980306

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=8 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+8))
    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 + 8}]]; a[n_] := b[n - 1, 0, 0];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 09 2017, after Alois P. Heinz *)