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A015544
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Lucas sequence U(5,-8): a(n+1)=5a(n)+8a(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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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 [From Paolo P. Lava (paoloplava(AT)gmail.com), Aug 05 2008]
G.f.: x/(1-5x-8x^2). [M. F. Hasler, Mar 06 2009]
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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 2}, {1, -6}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 19 2010]
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PROG
| (PARI) A015544(n)=imag((2+quadgen(57))^n) [M. F. Hasler, Mar 06 2009]
(Other) sage: [lucas_number1(n, 5, -8) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
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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: A050915 A091056 A197675 * A155597 A164538 A197533
Adjacent sequences: A015541 A015542 A015543 * A015545 A015546 A015547
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| More precise definition by M. F. Hasler (www.univ-ag.fr/~mhasler), Mar 06 2009
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