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A099100 a(n) = Fibonacci(5*n+1). 11
1, 8, 89, 987, 10946, 121393, 1346269, 14930352, 165580141, 1836311903, 20365011074, 225851433717, 2504730781961, 27777890035288, 308061521170129, 3416454622906707, 37889062373143906, 420196140727489673, 4660046610375530309, 51680708854858323072, 573147844013817084101, 6356306993006846248183 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Tanya Khovanova, Recursive Sequences
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
Sequence in context: A240457 A319842 A072352 * A208265 A184756 A295244
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Sep 29 2004
STATUS
approved

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Last modified February 28 14:20 EST 2024. Contains 370400 sequences. (Running on oeis4.)