A022401 Fibonacci sequence beginning 1, 31.
1, 31, 32, 63, 95, 158, 253, 411, 664, 1075, 1739, 2814, 4553, 7367, 11920, 19287, 31207, 50494, 81701, 132195, 213896, 346091, 559987, 906078, 1466065, 2372143, 3838208, 6210351, 10048559, 16258910
Offset: 0
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Tanya Khovanova, Recursive Sequences
- Index entries for linear recurrences with constant coefficients, signature (1, 1).
Programs
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Magma
I:=[1, 31]; [n le 2 select I[n] else Self(n-1)+Self(n-2): n in [1..40]]; // Vincenzo Librandi, Oct 30 2014
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Mathematica
CoefficientList[Series[(1 + 30 x)/(1 - x - x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 30 2014 *) Table[Fibonacci[n + 2] + 29*Fibonacci[n], {n, 0, 50}] (* G. C. Greubel, Mar 01 2018 *) -
PARI
for(n=0, 40, print1(fibonacci(n+2) + 29*fibonacci(n), ", ")) \\ G. C. Greubel, Mar 01 2018
Formula
a(n) = A118654(5, n).
G.f.: (1+30*x)/(1-x-x^2). - Philippe Deléham, Nov 20 2008
a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-61+sqrt(5)) + (1+sqrt(5))^n*(61+sqrt(5)))) / sqrt(5). - Colin Barker, Mar 02 2018