A084330 a(0)=0, a(1)=1, a(n) = 31*a(n-1) - 29*a(n-2).

0, 1, 31, 932, 27993, 840755, 25251608, 758417953, 22778659911, 684144336604, 20547893297305, 617144506454939, 18535590794481264, 556706123941725953, 16720357709153547887, 502186611389449931860, 15082894579507494998937, 453006320234438296943107

Offset: 0

Author

Benoit Cloitre, Jun 21 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A030191.

Programs

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

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 *)

PARI

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

Formula

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

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

Extensions

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