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A084329 a(0)=0, a(1)=1, a(n)=20a(n-1)-20a(n-2). 1
0, 1, 20, 380, 7200, 136400, 2584000, 48952000, 927360000, 17568160000, 332816000000, 6304956800000, 119442816000000, 2262757184000000, 42866287360000000, 812070603520000000, 15384086323200000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..16.

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, Jun 16 2008

MATHEMATICA

Union[Flatten[NestList[{#[[2]], 20(#[[2]]-#[[1]])}&, {0, 1}, 20]]]  (* Harvey P. Dale, Feb 24 2011 *)

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

CROSSREFS

Cf. A030191.

Sequence in context: A019580 A177109 A162806 * A097832 A163124 A163454

Adjacent sequences:  A084326 A084327 A084328 * A084330 A084331 A084332

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jun 21 2003

STATUS

approved

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Last modified October 20 13:57 EDT 2018. Contains 316379 sequences. (Running on oeis4.)