A194720 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting eight doublets into the initially empty word.

0, 1, 6435, 381333, 5068915, 33563481, 148733571, 507709165, 1443039123, 3581326065, 8006545891, 16475259141, 31690921395, 57644499913, 100028603715, 166732334301, 268424064211, 419229350625, 637511191203, 946759829365, 1376599316211, 1963918036281

Offset

0,3

Links

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

Formula

G.f.: x * (1 +6427*x +329881*x^2 +2198375*x^3 +3329195*x^4 +1251089*x^5 +91803*x^6 +429*x^7) / (x-1)^8.

a(0) = 0, a(n) = 1 +(14 +(90 +(350 +(910 +(1638 +(2002 +1430 * (n-1)) * (n-1)) * (n-1)) * (n-1)) * (n-1)) * (n-1)) * (n-1) for n>0.

Example

a(1) = 1: a^16 (with 1-ary alphabet {a}).

Maple

a:= n-> `if`(n=0, 0, (x-> 1+(14+(90+(350+(910+(1638+(2002+1430*x)*
                             x)*x)*x)*x)*x)*x)(n-1)):
seq(a(n), n=0..30);

Crossrefs

Row n=8 of A183134.

Sequence in context: A222554 A104318 A222344 * A140916 A208621 A294855

Adjacent sequences: A194717 A194718 A194719 * A194721 A194722 A194723

Keyword

nonn

Author

Alois P. Heinz, Sep 02 2011

Status

approved