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A159289
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a(n+1) = 5*a(n) - 2*a(n-1).
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3
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5, 21, 95, 433, 1975, 9009, 41095, 187457, 855095, 3900561, 17792615, 81161953, 370224535, 1688798769, 7703544775, 35140126337, 160293542135, 731187458001, 3335350205735, 15214376112673, 69401180151895, 316577148534129
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OFFSET
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0,1
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5, -2).
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FORMULA
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From R. J. Mathar, Apr 10 2009: (Start)
G.f.: -(-5+4*x)/(1-5*x+2*x^2).
a(n) = 5*A107839(n) - 4*A107839(n-1). (End)
a(n) = (5/2)*((5/2 + (1/2)*sqrt(17))^n + (5/2 - (1/2)*sqrt(17))^n) + (1/2)*sqrt(17)*((5/2 + (1/2)*sqrt(17))^n - (5/2 - (1/2)*sqrt(17))^n), with n >= 0. - Paolo P. Lava, Jul 31 2009
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MATHEMATICA
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LinearRecurrence[{5, -2}, {5, 21}, 50] (* G. C. Greubel, Jun 27 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(-(-5+4*x)/(1-5*x+2*x^2)) \\ G. C. Greubel, Jun 27 2018
(Magma) I:=[5, 21]; [n le 2 select I[n] else 5*Self(n-1) - 2*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 27 2018
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CROSSREFS
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Cf. A107839.
Sequence in context: A178876 A202513 A343349 * A201869 A017968 A017969
Adjacent sequences: A159286 A159287 A159288 * A159290 A159291 A159292
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KEYWORD
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nonn,easy
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AUTHOR
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Creighton Dement, Apr 08 2009
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STATUS
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approved
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