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Search: id:A084329
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| A084329 |
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a(0)=0, a(1)=1, a(n)=20a(n-1)-20a(n-2). |
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+0
2
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| 0, 1, 20, 380, 7200, 136400, 2584000, 48952000, 927360000, 17568160000, 332816000000, 6304956800000, 119442816000000, 2262757184000000, 42866287360000000, 812070603520000000, 15384086323200000000
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n)=(1/8)*sum(k=0, n, binomial(n, k)*F(6*k)) where F(k) denotes the k-th Fibonacci number.
G.f.: x/(1-20x+20x^2).
a(n)=-(1/40)*[10-4*sqrt(5)]^n*sqrt(5)+(1/40)*sqrt(5)*[10+4*sqrt(5)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 16 2008
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PROGRAM
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(PARI) a(n)=(1/8)*sum(k=0, n, binomial(n, k)*fibonacci(6*k))
(PARI) a(n)=imag((6+8*quadgen(5))^n)/8
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CROSSREFS
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Cf. A030191.
Adjacent sequences: A084326 A084327 A084328 this_sequence A084330 A084331 A084332
Sequence in context: A014901 A000564 A019580 this_sequence A097832 A063815 A075843
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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), Jun 21 2003
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