A022125 Fibonacci sequence beginning 3, 14.

3, 14, 17, 31, 48, 79, 127, 206, 333, 539, 872, 1411, 2283, 3694, 5977, 9671, 15648, 25319, 40967, 66286, 107253, 173539, 280792, 454331, 735123, 1189454, 1924577, 3114031, 5038608, 8152639, 13191247, 21343886, 34535133, 55879019, 90414152, 146293171, 236707323

Offset

0,1

Links

Colin Barker, 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

G.f.: (3 + 11*x)/(1 - x - x^2). - Philippe Deléham, Nov 19 2008

a(n) = h*Fibonacci(n+k) + Fibonacci(n+k-h) with h=6, k=2. - Bruno Berselli, Feb 20 2017

From Colin Barker, Feb 20 2017: (Start)

a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-25+3*sqrt(5)) + (1+sqrt(5))^n*(25+3*sqrt(5)))) / sqrt(5).

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

(End)

a(n) = Lucas(n+4) + Lucas(n-3). - Greg Dresden and Kathleen Wilson, Feb 28 2022

Mathematica

LinearRecurrence[{1, 1}, {3, 14}, 40] (* Harvey P. Dale, Oct 24 2013 *)

Prog

(PARI) Vec((3 + 11*x) / (1 - x - x^2) + O(x^50)) \\ Colin Barker, Feb 20 2017

Crossrefs

Cf. A000032, A000045.

Sequence in context: A022890 A032920 A134767 * A121459 A121226 A063633

Adjacent sequences: A022122 A022123 A022124 * A022126 A022127 A022128

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved