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A153593
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a(n) = ((9 + sqrt(2))^n - (9 - sqrt(2))^n)/(2*sqrt(2)).
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4
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1, 18, 245, 2988, 34429, 383670, 4186169, 45041112, 480032665, 5082340122, 53559541661, 562566880260, 5895000053461, 61667217421758, 644304909368225, 6725778192309168, 70163919621475249, 731614075994130210
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OFFSET
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1,2
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COMMENTS
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Eighth binomial transform of A048697.
lim_{n -> infinity} a(n)/a(n-1) = 9 + sqrt(2) = 10.4142135623....
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LINKS
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FORMULA
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a(n) = 18*a(n-1) - 79*a(n-2) for n>1; a(0)=0, a(1)=1. - Philippe Deléham, Jan 01 2009
G.f.: x/(1 - 18*x + 79*x^2). - Klaus Brockhaus, Dec 31 2008, corrected Oct 11 2009
a(n) = Sum[Binomial[n - 1 - i, i] (-1)^i * 18^(n - 1 - 2 i) * 79^i, {i, 0, Floor[(n - 1)/2]}]. - Sergio Falcon, Sep 21 2009
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MATHEMATICA
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LinearRecurrence[{18, -79}, {1, 18}, 25] (* G. C. Greubel, Aug 22 2016 *)
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PROG
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(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 31 2008
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Dec 29 2008
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EXTENSIONS
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STATUS
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approved
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