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Search: id:A049651
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| A049651 |
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a(n)=(F(3n+1)-1)/2, where F=A000045 (the Fibonacci sequence). |
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+0
2
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| 0, 1, 6, 27, 116, 493, 2090, 8855, 37512, 158905, 673134, 2851443, 12078908, 51167077, 216747218, 918155951, 3889371024, 16475640049, 69791931222, 295643364939, 1252365390980, 5305104928861, 22472785106426
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OFFSET
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0,3
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 24.
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FORMULA
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a(n)=4*a(n-1)+a(n-2)+2, a(0)=0, a(1)=1. G.f.: x*(x+1)/((x-1)*(x^2+4*x-1)). a(n) is asymptotic to -1/2+(sqrt(5)+5)/20*(sqrt(5)+2)^n. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 23 2003
a(n+1) = F(2) + F(5) + F(8) + ... + F(3n+2).
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CROSSREFS
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Cf. A033887.
Pairwise sums of A049652.
Sequence in context: A141844 A079742 A130019 this_sequence A109114 A080619 A080620
Adjacent sequences: A049648 A049649 A049650 this_sequence A049652 A049653 A049654
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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