A263854 Number of 4-ascent sequences of length n with no consecutive repeated letters.

1, 1, 4, 20, 110, 670, 4470, 32440, 254490, 2146525, 19374399, 186356108, 1903188611, 20569046543, 234562076984, 2814847291152, 35461339995304, 467952904377739, 6455368497736153, 92919917495585794, 1393239845937756837, 21726457354762648604

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=4 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+4))
    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 + 4}]]; 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(21) from Alois P. Heinz, Nov 19 2015