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Search: id:A094704
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| A094704 |
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Convolution of Fibonacci(n) and 10^n. |
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+0
1
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| 0, 1, 11, 112, 1123, 11235, 112358, 1123593, 11235951, 112359544, 1123595495, 11235955039, 112359550534, 1123595505573, 11235955056107, 112359550561680, 1123595505617787, 11235955056179467, 112359550561797254
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OFFSET
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0,3
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COMMENT
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The convolution of Fibonacci(n) and k^n for k>1 has a(n)=((1/2-sqrt(5)/2)^n((k+2)sqrt(5)/10-k/2)- (1/2+sqrt(5)/2)^n((k+2)sqrt(5)/10+k/2)+k^(n+1))/(k^2-k-1).
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FORMULA
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G.f. : x/((1-x-x^2)(1-10x)); a(n)=10^(n+1)/89+(1/2-sqrt(5)/2)^n(6sqrt(5)/445-5/89)-(1/2+sqrt(5)/2)^n(6sqrt(5)/445+5/89).
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CROSSREFS
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Cf. A019523.
Sequence in context: A065834 A104720 A132926 this_sequence A019523 A132939 A059996
Adjacent sequences: A094701 A094702 A094703 this_sequence A094705 A094706 A094707
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 21 2004
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