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A084330 a(0)=0, a(1)=1, a(n) = 31*a(n-1) - 29*a(n-2). 2
0, 1, 31, 932, 27993, 840755, 25251608, 758417953, 22778659911, 684144336604, 20547893297305, 617144506454939, 18535590794481264, 556706123941725953, 16720357709153547887, 502186611389449931860, 15082894579507494998937, 453006320234438296943107 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Karl V. Keller, Jr., Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (31,-29).

FORMULA

a(n) = (1/13)*sum(k=0, n, binomial(n, k)*F(7*k)) where F(k) denotes the k-th Fibonacci number.

a(n) = (1/65)*(31/2+(13/2)*sqrt(5))^n*sqrt(5)-(1/65)*sqrt(5)*(31/2-(13/2)*sqrt(5))^n, with n>=0. - Paolo P. Lava, Jun 17 2008

G.f.: x / (29*x^2-31*x+1). - Colin Barker, Jun 26 2013

MAPLE

f:=proc(n) option remember; if n <=1 then n else 31*f(n-1)-29*f(n-2); fi; end;

MATHEMATICA

LinearRecurrence[{31, -29}, {0, 1}, 30] (* Harvey P. Dale, Jul 11 2014 *)

PROG

(PARI) a(n)=(1/13)*sum(k=0, n, binomial(n, k)*fibonacci(7*k))

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 31*Self(n-1)-29*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 02 2015

CROSSREFS

Cf. A030191.

Sequence in context: A170712 A170750 A218733 * A238993 A171336 A200442

Adjacent sequences:  A084327 A084328 A084329 * A084331 A084332 A084333

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Jun 21 2003

EXTENSIONS

Corrected by N. J. A. Sloane, Sep 16 2005

STATUS

approved

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Last modified August 3 00:25 EDT 2021. Contains 346429 sequences. (Running on oeis4.)