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Search: id:A099013
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| A099013 |
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Sum k=0..n, 3^(k-1)Fib(k). |
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+0
2
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| 0, 1, 4, 22, 103, 508, 2452, 11929, 57856, 280930, 1363495, 6618856, 32128024, 155953777, 757013548, 3674624638, 17836995847, 86582609284, 420280790476, 2040085854985, 9902784679240, 48069126732586, 233332442310919
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Partial sums of A099012. Binomial transform of A063092 (with leading 0).
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FORMULA
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G.f.: x/((1-x)(1-3x-9x^2)); a(n)=4a(n-1)+6a(n-2)+9a(n-3); a(n)=3^(n-1)*sum{k=0..n, Fib(n-k)3^(-k)}; a(n)=(3/2+3sqrt(5)/2)^n(1/22+7sqrt(5)/110)+(1/22-7sqrt(5)/110)(3/2-3sqrt(5)/2)^n-1/11.
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CROSSREFS
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Cf. A000045.
Adjacent sequences: A099010 A099011 A099012 this_sequence A099014 A099015 A099016
Sequence in context: A007901 A088581 A017970 this_sequence A001436 A024420 A108840
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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), Sep 22 2004
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