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

0,2

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).

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

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 *)

Prog

(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
(PARI) for(n=0, 40, print1(fibonacci(n+2) + 29*fibonacci(n), ", ")) \\ G. C. Greubel, Mar 01 2018

Crossrefs

Sequence in context: A291523 A256496 A133782 * A042936 A042934 A042930

Adjacent sequences: A022398 A022399 A022400 * A022402 A022403 A022404

Keyword

nonn

Author

N. J. A. Sloane

Status

approved