A022380 Fibonacci sequence beginning 3, 12.

3, 12, 15, 27, 42, 69, 111, 180, 291, 471, 762, 1233, 1995, 3228, 5223, 8451, 13674, 22125, 35799, 57924, 93723, 151647, 245370, 397017, 642387, 1039404, 1681791, 2721195, 4402986, 7124181, 11527167, 18651348, 30178515, 48829863, 79008378

Offset

0,1

Links

Indranil Ghosh, Table of n, a(n) for n = 0..4771

Tanya Khovanova, Recursive Sequences

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

Formula

G.f.: (3+9*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = ((2^(-n-1)/5)*((15+21*sqrt(5))*(1+sqrt(5))^n + (15-21*sqrt(5))*(1-sqrt(5))^n). - Bogart B. Strauss, Oct 27 2013

a(n) = -(3/2)*(A000045(n+1)-3*A000032(n+1)). - Harvey P. Dale, Aug 22 2019

a(n) = 3*A000285(n). - R. J. Mathar, Jan 08 2020

Mathematica

a[0]=3; a[1] = 12; a[n_]:= a[n-1] +  a[n-2]; Table[a[n], {n, 0, 30}] (* or *) LinearRecurrence[{1, 1}, {3, 12}, 31] (* Indranil Ghosh, Feb 19 2017 *)
Table[-(3/2)(Fibonacci[n]-3*LucasL[ n]), {n, 40}] (* Harvey P. Dale, Aug 22 2019 *)

Prog

(Magma) [-(3/2)*(Fibonacci(n+1)-3*Lucas(n+1)): n in [0..40]]; // Vincenzo Librandi, Jan 09 2020

Crossrefs

Sequence in context: A248105 A269315 A329575 * A331074 A290593 A005392

Adjacent sequences: A022377 A022378 A022379 * A022381 A022382 A022383

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved