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Search: id:A015544
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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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+0
2
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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; listen)
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OFFSET
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0,3
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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 [From Paolo P. Lava (ppl(AT)spl.at), Aug 05 2008]
G.f.: x/(1-5x-8x^2). [M. F. Hasler, Mar 06 2009]
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PROGRAM
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(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
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Sequence in context: A146263 A050915 A091056 this_sequence A155597 A164538 A083076
Adjacent sequences: A015541 A015542 A015543 this_sequence A015545 A015546 A015547
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
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More precise definition by M. F. Hasler (MHasler(AT)univ-ag.fr), Mar 06 2009
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