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A022380 Fibonacci sequence beginning 3, 12. 2
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 (list; graph; refs; listen; history; text; internal format)
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]

MATHEMATICA

a={}; b=3; c=12; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 4!}]; a (* Vladimir Joseph Stephan Orlovsky, Sep 18 2008 *)

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 *)

CROSSREFS

Sequence in context: A044828 A248105 A269315 * A005392 A001196 A096854

Adjacent sequences:  A022377 A022378 A022379 * A022381 A022382 A022383

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 24 02:34 EDT 2017. Contains 288697 sequences.