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A264916 Number of n-ascent sequences of length n with no consecutive repeated letters. 2
1, 1, 2, 12, 110, 1380, 21931, 422128, 9544164, 247924425, 7276062838, 238094692473, 8595519551905, 339369780700496, 14547197878632067, 672813893127964088, 33396560680565891888, 1770862858604836365591, 99902715110909008145856, 5974701996798223000294793 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Nov 09 2017, after Alois P. Heinz *)

CROSSREFS

Main diagonal of A264909.

Sequence in context: A217802 A126778 A158832 * A296644 A235860 A317208

Adjacent sequences:  A264913 A264914 A264915 * A264917 A264918 A264919

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 28 2015

STATUS

approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)