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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, 18651348, 30178515, 48829863, 79008378 (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 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 STATUS approved

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Last modified October 20 23:28 EDT 2020. Contains 337910 sequences. (Running on oeis4.)