A099100 a(n) = Fibonacci(5*n+1).

1, 8, 89, 987, 10946, 121393, 1346269, 14930352, 165580141, 1836311903, 20365011074, 225851433717, 2504730781961, 27777890035288, 308061521170129, 3416454622906707, 37889062373143906, 420196140727489673, 4660046610375530309, 51680708854858323072, 573147844013817084101, 6356306993006846248183

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (11,1).

Formula

G.f.: (1 - 3*x)/(1 - 11*x - x^2);

a(n) = 11*a(n-1) + a(n-2). [corrected by Philippe Deléham, Nov 16 2008]

a(n) = Sum_{k=0..5*n} binomial(k, 5*n-k).

2*a(n) = Fibonacci(5*n) + Lucas(5*n). - Bruno Berselli, Oct 13 2017

Maple

with(combinat): A099100:=n->fibonacci(5*n+1): seq(A099100(n), n=0..20); # Wesley Ivan Hurt, Nov 18 2014

Mathematica

Fibonacci/@(5*Range[0, 30]+1) (* Vladimir Joseph Stephan Orlovsky, Mar 01 2010 *)

Prog

(Magma) [Fibonacci(5*n+1): n in [0..100]]; // Vincenzo Librandi, Apr 16 2011
(PARI) a(n)=fibonacci(5*n+1) \\ Charles R Greathouse IV, Sep 28 2015

Crossrefs

Cf. A000032, A000045.

Sequence in context: A240457 A319842 A072352 * A208265 A184756 A295244

Adjacent sequences: A099097 A099098 A099099 * A099101 A099102 A099103

Keyword

nonn,easy

Author

Paul Barry, Sep 29 2004

Status

approved