A264914 - OEIS

%I #12 Nov 09 2017 11:39:11

%S 1,1,9,90,945,10440,121065,1470855,18688680,247924425,3428559573,

%T 49353455856,738477897552,11471175099726,184755890053173,

%U 3081830366508444,53182355345412138,948482464405185843,17465164002387664056,331740754587283644945,6494261833979742949884

%N Number of 9-ascent sequences of length n with no consecutive repeated letters.

%H Alois P. Heinz, <a href="/A264914/b264914.txt">Table of n, a(n) for n = 0..200</a>

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

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

%p       `if`(j=i, 0, b(n-1, j, t+`if`(j>i, 1, 0))), j=0..t+9))

%p     end:

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

%p seq(a(n), n=0..30);

%t 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 + 9}]]; a[n_] := b[n - 1, 0, 0];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Nov 09 2017, after _Alois P. Heinz_ *)

%Y Column k=9 of A264909.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Nov 28 2015