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 A015544 Lucas sequence U(5,-8): a(n+1) = 5*a(n) + 8*a(n-1), a(0)=0, a(1)=1. 3
 0, 1, 5, 33, 205, 1289, 8085, 50737, 318365, 1997721, 12535525, 78659393, 493581165, 3097180969, 19434554165, 121950218577, 765227526205, 4801739379641, 30130517107845, 189066500576353, 1186376639744525, 7444415203333449, 46713089134623445 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,8). FORMULA a(n) = 5*a(n-1) + 8*a(n-2). a(n) = (1/57)*sqrt(57)*[5/2 + (1/2)*sqrt(57)]^n - (1/57)*sqrt(57)*[5/2 - (1/2)*sqrt(57)]^n, with n>=0. - Paolo P. Lava, Aug 05 2008 G.f.: x/(1 - 5*x - 8*x^2). - M. F. Hasler, Mar 06 2009 MATHEMATICA a[n_]:=(MatrixPower[{{1, 2}, {1, -6}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *) LinearRecurrence[{5, 8}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *) PROG (PARI) A015544(n)=imag((2+quadgen(57))^n) \\ M. F. Hasler, Mar 06 2009 (Sage) [lucas_number1(n, 5, -8) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009 (MAGMA) [n le 2 select n-1 else 5*Self(n-1) + 8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012 (PARI) x='x+O('x^30); concat([0], Vec(x/(1 - 5*x - 8*x^2))) \\ G. C. Greubel, Jan 01 2018 CROSSREFS Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015441, A015443, A015447, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226. Sequence in context: A091056 A244901 A197675 * A155597 A250163 A164538 Adjacent sequences:  A015541 A015542 A015543 * A015545 A015546 A015547 KEYWORD nonn,easy AUTHOR EXTENSIONS More precise definition by M. F. Hasler, Mar 06 2009 STATUS approved

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Last modified April 13 19:13 EDT 2021. Contains 342939 sequences. (Running on oeis4.)