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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000032, A000045.

Programs

Mathematica

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

PARI

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

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