A194721 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting nine doublets into the initially empty word.

0, 1, 24310, 2699837, 52955950, 464221105, 2561439806, 10466643805, 34648845862, 98156060225, 246643289830, 563506356061, 1191627482750, 2363434581937, 4441172224750, 7969478316605, 13742556531766, 22888430598145, 36972962559062, 58126513174525, 89196318660430

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: -x * (1 +24301*x +2481083*x^2 +29532493*x^3 +82769773*x^4 +66140687*x^5 +14462017*x^6 +624055*x^7 +1430*x^8) / (x-1)^9.

a(0) = 0, a(n) = 1 +(16 +(119 +(544 +(1700 +(3808 +(6188 +(7072 +4862 * (n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1) for n>0.

Example

a(1) = 1: a^18 (with 1-ary alphabet {a}).

Maple

a:= n-> `if`(n=0, 0, (x-> 1+(16+(119+(544+(1700+(3808+(6188+(7072+4862
                          *x)*x)*x)*x)*x)*x)*x)*x)(n-1)):
seq(a(n), n=0..30);

Crossrefs

Row n=9 of A183134.

Sequence in context: A078870 A154069 A318630 * A140923 A208622 A294856

Adjacent sequences: A194718 A194719 A194720 * A194722 A194723 A194724

Keyword

nonn

Author

Alois P. Heinz, Sep 02 2011

Status

approved