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

Author

Alois P. Heinz, Nov 28 2015

Keywords

• nonn

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.

Crossrefs

Main diagonal of A264909.

Programs

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 *)

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