A264916 Number of n-ascent sequences of length n with no consecutive repeated letters.

1, 1, 2, 12, 110, 1380, 21931, 422128, 9544164, 247924425, 7276062838, 238094692473, 8595519551905, 339369780700496, 14547197878632067, 672813893127964088, 33396560680565891888, 1770862858604836365591, 99902715110909008145856, 5974701996798223000294793

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..125

S. Kitaev, J. Remmel, p-Ascent Sequences, arXiv:1503.00914 [math.CO], 2015.

Formula

a(n) = A264909(n,n).

a(n) ~ c * n! * d^n / n^(3/2), where d = 3.4022754519536669374151613210346790003... and c = 0.34285335011727623741388891327237... - Vaclav Kotesovec, Aug 14 2017

Maple

b:= proc(n, k, i, t) option remember; `if`(n<1, 1, add(
      `if`(j=i, 0, b(n-1, k, j, t+`if`(j>i, 1, 0))), j=0..t+k))
    end:
a:= n-> b(n-1, n, 0$2):
seq(a(n), n=0..25);

Mathematica

b[n_, k_, i_, t_] := b[n, k, i, t] = If[n < 1, 1, Sum[If[j == i, 0, b[n - 1, k, j, t + If[j > i, 1, 0]]], {j, 0, t + k}]];
a[n_] := b[n - 1, n, 0, 0];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Nov 09 2017, after Alois P. Heinz *)

Crossrefs

Main diagonal of A264909.

Sequence in context: A126778 A158832 A372158 * A296644 A235860 A317208

Adjacent sequences: A264913 A264914 A264915 * A264917 A264918 A264919

Keyword

nonn

Author

Alois P. Heinz, Nov 28 2015

Status

approved