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A015544
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Lucas sequence U(5,-8): a(n+1) = 5*a(n) + 8*a(n-1), a(0)=0, a(1)=1.
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3
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0, 1, 5, 33, 205, 1289, 8085, 50737, 318365, 1997721, 12535525, 78659393, 493581165, 3097180969, 19434554165, 121950218577, 765227526205, 4801739379641, 30130517107845, 189066500576353, 1186376639744525, 7444415203333449, 46713089134623445
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,8).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gérard
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EXTENSIONS
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More precise definition by M. F. Hasler, Mar 06 2009
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STATUS
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approved
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