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A022401 Fibonacci sequence beginning 1, 31. 2
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 (list; graph; refs; listen; history; text; internal format)
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) = 31*A000045(n) + A000045(n-1). - Paolo P. Lava, May 19 2015

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

MAPLE

with(numtheory): with(combinat): P:=proc(q) local n;

for n from 0 to q do print(31*fibonacci(n)+fibonacci(n-1));

od; end: P(30); # Paolo P. Lava, May 19 2015

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

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Last modified December 10 19:01 EST 2018. Contains 318049 sequences. (Running on oeis4.)