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A097165 Expansion of (1-3x)/((1-x)(1-4x)(1-5x)). +0
4
1, 7, 41, 227, 1221, 6447, 33601, 173467, 889181, 4533287, 23015961, 116477907, 587981941, 2962279327, 14900875121, 74862289547, 375743103501, 1884442140567, 9445117195081, 47317211944387, 236952563597861 (list; graph; listen)
OFFSET

0,2

COMMENT

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.

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).

CROSSREFS

Sequence in context: A084779 A081625 A144635 this_sequence A152268 A026002 A057009

Adjacent sequences: A097162 A097163 A097164 this_sequence A097166 A097167 A097168

KEYWORD

easy,nonn

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Jul 30 2004

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Last modified November 25 14:49 EST 2009. Contains 167514 sequences.


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