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Search: id:A111262
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| A111262 |
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a(n)=(1/n)*sum(k=1,n,F(4k)B(2n-2k)binomial(2n,2k)), where F are Fibonacci numbers and B are Bernoulli numbers. |
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4
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| 3, 12, 65, 403, 2652, 17889, 121859, 833260, 5706081, 39096531, 267936188, 1836369217, 12586419075, 86267964108, 591287758337, 4052742230419, 27777897084444, 190392509164065, 1304969593244291, 8944394450283436
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OFFSET
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1,1
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COMMENT
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Values are always integers.
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FORMULA
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a(n)=F(4n-2)+2F(2n-1); recurrence : a(n)=10a(n-1)-23a(n-2)+10a(n-3)-a(n-4)
O.g.f.: -x*(-3+18*x-14*x^2+x^3)/((x^2-3*x+1)*(x^2-7*x+1)) = -1+(2-4*x)/(x^2-3*x+1)+(-1+8*x)/(x^2-7*x+1) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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PROGRAM
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(PARI) a(n)=fibonacci(4*n-2)+2*fibonacci(2*n-1)
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CROSSREFS
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Cf. A001519.
Adjacent sequences: A111259 A111260 A111261 this_sequence A111263 A111264 A111265
Sequence in context: A124562 A052757 A029851 this_sequence A139134 A109577 A007017
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 12 2005, corrected Feb 24 2008
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