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

0,3

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).

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.

Example

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

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 *)

Crossrefs

Row n=6 of A183134.

Sequence in context: A364848 A027816 A027823 * A267283 A289349 A023912

Adjacent sequences: A194715 A194716 A194717 * A194719 A194720 A194721

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 02 2011

Status

approved