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A022127 Fibonacci sequence beginning 3, 17. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A173579 A093024

Adjacent sequences:  A022124 A022125 A022126 * A022128 A022129 A022130

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 30 22:34 EDT 2017. Contains 285687 sequences.