A264915 - OEIS

%I #12 Nov 09 2017 11:39:18

%S 1,1,10,110,1265,15235,191785,2519605,34494625,491432590,7276062838,

%T 111816814439,1781492191281,29392907305322,501677394880530,

%U 8849027884862077,161155012811798819,3027460412190175918,58617635130507630386,1168800382939975874066

%N Number of 10-ascent sequences of length n with no consecutive repeated letters.

%H Alois P. Heinz, <a href="/A264915/b264915.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+10))

%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 + 10}]]; 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=10 of A264909.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Nov 28 2015