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
Links
- Tanya Khovanova, Recursive Sequences
- Index entries for linear recurrences with constant coefficients, signature (11,1).
Programs
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Magma
[Fibonacci(5*n+1): n in [0..100]]; // Vincenzo Librandi, Apr 16 2011
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Maple
with(combinat): A099100:=n->fibonacci(5*n+1): seq(A099100(n), n=0..20); # Wesley Ivan Hurt, Nov 18 2014
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Mathematica
Fibonacci/@(5*Range[0,30]+1) (* Vladimir Joseph Stephan Orlovsky, Mar 01 2010 *)
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PARI
a(n)=fibonacci(5*n+1) \\ Charles R Greathouse IV, Sep 28 2015
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