A194717 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting five doublets into the initially empty word.

0, 1, 126, 1181, 4966, 14289, 32966, 65821, 118686, 198401, 312814, 470781, 682166, 957841, 1309686, 1750589, 2294446, 2956161, 3751646, 4697821, 5812614, 7114961, 8624806, 10363101, 12351806, 14613889, 17173326, 20055101, 23285206, 26890641, 30899414, 35340541

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 (5,-10,10,-5,1).

Formula

G.f.: -x*(1+121*x+561*x^2+311*x^3+14*x^4) / (x-1)^5.

a(0) = 0, a(n) = 1+(8+(27+(48+42*(n-1))*(n-1))*(n-1))*(n-1) for n>0.

Example

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

Maple

a:= n-> `if`(n=0, 0, (x-> 1+(8+(27+(48+42*x)*x)*x)*x)(n-1)):
seq(a(n), n=0..40);

Crossrefs

Row n=5 of A183134.

Sequence in context: A104678 A154093 A172139 * A002953 A216588 A297657

Adjacent sequences: A194714 A194715 A194716 * A194718 A194719 A194720

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 02 2011

Status

approved