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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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1
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0, 1, 20, 380, 7200, 136400, 2584000, 48952000, 927360000, 17568160000, 332816000000, 6304956800000, 119442816000000, 2262757184000000, 42866287360000000, 812070603520000000, 15384086323200000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| 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 (paoloplava(AT)gmail.com), Jun 16 2008
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MATHEMATICA
| Union[Flatten[NestList[{#[[2]], 20(#[[2]]-#[[1]])}&, {0, 1}, 20]]] (* From Harvey P. Dale, Feb 24 2011 *)
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PROG
| (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
| Cf. A030191.
Sequence in context: A019580 A177109 A162806 * A097832 A163124 A163454
Adjacent sequences: A084326 A084327 A084328 * A084330 A084331 A084332
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 21 2003
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