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A097165
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Expansion of (1-3x)/((1-x)(1-4x)(1-5x)).
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3
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1, 7, 41, 227, 1221, 6447, 33601, 173467, 889181, 4533287, 23015961, 116477907, 587981941, 2962279327, 14900875121, 74862289547, 375743103501, 1884442140567, 9445117195081, 47317211944387, 236952563597861
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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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).
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MATHEMATICA
| CoefficientList[Series[(1-3x)/((1-x)(1-4x)(1-5x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{10, -29, 20}, {1, 7, 41}, 30] (* From Harvey P. Dale, Jan 24 2012 *)
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CROSSREFS
| Sequence in context: A191010 A081625 A144635 * A152268 A026002 A173409
Adjacent sequences: A097162 A097163 A097164 * A097166 A097167 A097168
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 30 2004
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