A194718 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting six doublets into the initially empty word.

0, 1, 462, 7941, 48838, 185193, 530526, 1265677, 2654646, 5060433, 8960878, 14964501, 23826342, 36463801, 53972478, 77642013, 108971926, 149687457, 201755406, 267399973, 349118598, 449697801, 572229022, 720124461, 897132918, 1107355633, 1355262126, 1645706037

Offset: 0

Author

Alois P. Heinz, Sep 02 2011

Keywords

• nonn
• easy

Examples

			a(1) = 1: aaaaaaaaaaaa (with 1-ary alphabet {a}).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Crossrefs

Row n=6 of A183134.

Programs

Maple

a:= n-> `if`(n=0, 0, (x-> 1+(10+(44+(110+(165+132*x)*x)*x)*x)*x)(n-1)):
seq(a(n), n=0..30);

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,462,7941,48838,185193,530526},30] (* Harvey P. Dale, Oct 23 2015 *)

Formula

G.f.: x*(1+456*x+5184*x^2+8102*x^3+2055*x^4+42*x^5) / (x-1)^6.

a(0) = 0, a(n) = 1+(10+(44+(110+(165+132*(n-1))*(n-1))*(n-1))*(n-1)) * (n-1) for n>0.