A097165 Expansion of (1-3x)/((1-x)(1-4x)(1-5x)).

1, 7, 41, 227, 1221, 6447, 33601, 173467, 889181, 4533287, 23015961, 116477907, 587981941, 2962279327, 14900875121, 74862289547, 375743103501, 1884442140567, 9445117195081, 47317211944387, 236952563597861

Offset

0,2

Comments

Partial sums of A085351. Convolution of A034478 and 4^n. Convolution of A047849 and 5^n. a(n)=A097162(2n+1)/3. Third binomial transform of A097164.

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (10,-29,20).

Formula

a(n)=5*5^n/2-4*4^n/3-1/6; a(n)=sum{k=0..n, (5^k+1)4^(n-k)/2}; a(n)=sum{k=0..n, (4^k+2)5^(n-k)/3}; a(n)=10a(n-1)-29a(n-2)+20a(n-3).

Mathematica

CoefficientList[Series[(1-3x)/((1-x)(1-4x)(1-5x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{10, -29, 20}, {1, 7, 41}, 30] (* Harvey P. Dale, Jan 24 2012 *)

Crossrefs

Sequence in context: A239041 A081625 A144635 * A152268 A026002 A173409

Adjacent sequences: A097162 A097163 A097164 * A097166 A097167 A097168

Keyword

easy,nonn

Author

Paul Barry, Jul 30 2004

Status

approved