A022127 Fibonacci sequence beginning 3, 17.

3, 17, 20, 37, 57, 94, 151, 245, 396, 641, 1037, 1678, 2715, 4393, 7108, 11501, 18609, 30110, 48719, 78829, 127548, 206377, 333925, 540302, 874227, 1414529, 2288756, 3703285, 5992041, 9695326, 15687367, 25382693, 41070060, 66452753, 107522813, 173975566

Offset

0,1

Links

Indranil Ghosh, Table of n, a(n) for n = 0..4770

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (1, 1).

Formula

G.f.: (3 + 14*x) / (1 - x - x^2). - Philippe Deléham, Nov 19 2008

From Colin Barker, Feb 21 2017: (Start)

a(n) = 2^(-1-n)*((1-sqrt(5))^n*(-31+3*sqrt(5)) + (1+sqrt(5))^n*(31+3*sqrt(5))) / sqrt(5).

a(n) = a(n-1) + a(n-2) for n>1.

(End)

Mathematica

LinearRecurrence[{1, 1}, {3, 17}, 31] (* or *) CoefficientList[Series[(3+14x)/(1-x-x^2) , {x, 0, 30}], x] (* or *) a[0] = 3; a[1] = 17; a[n_]:=a[n-2]+ a[n-1]; Table[a[n], {n, 0, 30}] (* Indranil Ghosh, Feb 20 2017 *)

Prog

(PARI) Vec((3 + 14*x) / (1 - x - x^2) + O(x^30)) \\ Colin Barker, Feb 21 2017

Crossrefs

Sequence in context: A147845 A077778 A273420 * A273448 A298469 A173579

Adjacent sequences: A022124 A022125 A022126 * A022128 A022129 A022130

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved