A264914 Number of 9-ascent sequences of length n with no consecutive repeated letters.

1, 1, 9, 90, 945, 10440, 121065, 1470855, 18688680, 247924425, 3428559573, 49353455856, 738477897552, 11471175099726, 184755890053173, 3081830366508444, 53182355345412138, 948482464405185843, 17465164002387664056, 331740754587283644945, 6494261833979742949884

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=9 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+9))
    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 + 9}]]; a[n_] := b[n - 1, 0, 0];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 09 2017, after Alois P. Heinz *)