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A154236
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a(n) = ( (5 + sqrt(6))^n - (5 - sqrt(6))^n )/(2*sqrt(6)).
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2
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1, 10, 81, 620, 4661, 34830, 259741, 1935640, 14421321, 107436050, 800355401, 5962269060, 44415937981, 330876267670, 2464859855061, 18361949464880, 136787157402641, 1018994534193690, 7590989351286721, 56548997363187100
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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 + sqrt(6) = 7.4494897427....
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LINKS
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FORMULA
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a(n) = 10*a(n-1) - 19*a(n-2) for n > 1, with a(0)=0, a(1)=1.
G.f.: x/(1 - 10*x + 19*x^2). (End)
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MATHEMATICA
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LinearRecurrence[{10, -19}, {1, 10}, 25] (* or *) Table[Simplify[((5 + Sqrt[6])^n -(5-Sqrt[6])^n)/(2*Sqrt[6])], {n, 1, 25}] (* G. C. Greubel, Sep 06 2016 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((5+r)^n-(5-r)^n)/(2*r): n in [1..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
(Sage) [lucas_number1(n, 10, 19) for n in range(1, 25)] # Zerinvary Lajos, Apr 26 2009
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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 05 2009
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EXTENSIONS
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STATUS
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approved
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