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A022379 Fibonacci sequence beginning 3, 9. 5
3, 9, 12, 21, 33, 54, 87, 141, 228, 369, 597, 966, 1563, 2529, 4092, 6621, 10713, 17334, 28047, 45381, 73428, 118809, 192237, 311046, 503283, 814329, 1317612, 2131941, 3449553, 5581494, 9031047, 14612541, 23643588, 38256129, 61899717, 100155846, 162055563, 262211409 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..37.

Tanya Khovanova, Recursive Sequences

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

FORMULA

G.f.: (3 + 6*x)/(1 - x - x^2). - Philippe Deléham, Nov 19 2008

a(n+2) = 3*L(n+3) = L(n) + 4*L(n+1) + 2*L(n+2), where L=A000032. - J. M. Bergot, Oct 21 2012

a(n) = Fibonacci(n+4) - Fibonacci(n-4), where n>0 and Fibonacci(-3..-1) = 2,-1,1. - Bruno Berselli, May 22 2015

a(n) = L(n+4) + L(n-4) - 4*L(n) for n>0. - Bruno Berselli, Dec 29 2016

MATHEMATICA

LinearRecurrence[{1, 1}, {3, 9}, 30] (* Alonso del Arte, Oct 09 2013 *)

Table[3 LucasL[n + 1], {n, 0, 40}] (* Bruno Berselli, May 22 2015 *)

Table[LucasL[n + 4] + LucasL[n - 4] - 4 LucasL[n], {n, 1, 40}] (* Bruno Berselli, Dec 30 2016 *)

PROG

(PARI) Vec((3+6*x)/(1-x-x^2)+O(x^99)) \\ Charles R Greathouse IV, Oct 21 2012

(MAGMA) [3*Lucas(n+1): n in [0..40]]; // Bruno Berselli, May 22 2015

CROSSREFS

Cf. A000032, A000045.

Cf. similar sequences listed in A258160.

Sequence in context: A155504 A270672 A211217 * A261957 A261951 A081601

Adjacent sequences:  A022376 A022377 A022378 * A022380 A022381 A022382

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Bruno Berselli, May 22 2015

STATUS

approved

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Last modified July 25 14:33 EDT 2017. Contains 289795 sequences.