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A022125 Fibonacci sequence beginning 3, 14. 3
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 (list; graph; refs; listen; history; text; internal format)
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)

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. 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

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Last modified May 26 05:14 EDT 2017. Contains 287074 sequences.