A084329 a(0)=0, a(1)=1, a(n)=20a(n-1)-20a(n-2).

0, 1, 20, 380, 7200, 136400, 2584000, 48952000, 927360000, 17568160000, 332816000000, 6304956800000, 119442816000000, 2262757184000000, 42866287360000000, 812070603520000000, 15384086323200000000

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (20,-20).

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).

Mathematica

Union[Flatten[NestList[{#[[2]], 20(#[[2]]-#[[1]])}&, {0, 1}, 20]]]  (* Harvey P. Dale, Feb 24 2011 *)
LinearRecurrence[{20, -20}, {0, 1}, 20] (* Harvey P. Dale, Nov 29 2019 *)

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: A177109 A162806 A324949 * A097832 A342886 A163124

Adjacent sequences: A084326 A084327 A084328 * A084330 A084331 A084332

Keyword

nonn

Author

Benoit Cloitre, Jun 21 2003

Status

approved