A264916 - OEIS

%I #19 Nov 09 2017 11:39:27

%S 1,1,2,12,110,1380,21931,422128,9544164,247924425,7276062838,

%T 238094692473,8595519551905,339369780700496,14547197878632067,

%U 672813893127964088,33396560680565891888,1770862858604836365591,99902715110909008145856,5974701996798223000294793

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

%H Alois P. Heinz, <a href="/A264916/b264916.txt">Table of n, a(n) for n = 0..125</a>

%H S. Kitaev, J. Remmel, <a href="https://arxiv.org/abs/1503.00914">p-Ascent Sequences</a>, arXiv:1503.00914 [math.CO], 2015.

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

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

%p b:= proc(n, k, i, t) option remember; `if`(n<1, 1, add(

%p       `if`(j=i, 0, b(n-1, k, j, t+`if`(j>i, 1, 0))), j=0..t+k))

%p     end:

%p a:= n-> b(n-1, n, 0$2):

%p seq(a(n), n=0..25);

%t 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}]];

%t a[n_] := b[n - 1, n, 0, 0];

%t Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Nov 09 2017, after _Alois P. Heinz_ *)

%Y Main diagonal of A264909.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Nov 28 2015