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

0,3

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.

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 *)

Crossrefs

Column k=3 of A264909.

Sequence in context: A193115 A270489 A335819 * A266083 A245374 A052673

Adjacent sequences: A263850 A263851 A263852 * A263854 A263855 A263856

Keyword

nonn

Author

N. J. A. Sloane, Nov 18 2015

Extensions

a(10)-a(22) from Alois P. Heinz, Nov 19 2015

Status

approved