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A154340
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a(n) = ( (5 + 2*sqrt(2))^n - (5 - 2*sqrt(2))^n )/(4*sqrt(2)).
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1
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1, 10, 83, 660, 5189, 40670, 318487, 2493480, 19520521, 152816050, 1196311643, 9365243580, 73315137869, 573942237830, 4493065034527, 35173632302160, 275354217434641, 2155590425209690, 16874882555708003, 132103788328515300
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OFFSET
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1,2
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COMMENTS
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Lim_{n -> infinity} a(n)/a(n-1) = 5 + 2*sqrt(2) = 7.8284271247....
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LINKS
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FORMULA
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a(n) = 10*a(n-1) - 17*a(n-2) for n > 1, with a(0)=0, a(1)=1. - Philippe Deléham, Jan 12 2009
G.f.: x/(1 - 10*x + 17*x^2). - Klaus Brockhaus, Jan 12 2009, corrected Oct 08 2009
E.g.f.: (1/sqrt(8))*exp(5*x)*sinh(2*sqrt(2)*x). - G. C. Greubel, Sep 11 2016
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MAPLE
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MATHEMATICA
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LinearRecurrence[{10, -17}, {1, 10}, 30] (* or *) Table[Simplify[((5 + 2*Sqrt[2])^n -(5-2*Sqrt[2])^n)/(4*Sqrt[2])], {n, 1, 30}] (* G. C. Greubel, Sep 11 2016 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+2*r)^n-(5-2*r)^n)/(4*r): n in [1..30] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 12 2009
(Sage) [lucas_number1(n, 10, 17) for n in range(1, 30)] # Zerinvary Lajos, Apr 26 2009
(Magma) I:=[1, 10]; [n le 2 select I[n] else 10*Self(n-1)-17*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 12 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
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EXTENSIONS
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STATUS
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approved
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