A022379 Fibonacci sequence beginning 3, 9.

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

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: A270672 A211217 A307201 * A344720 A303192 A261957

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