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A147960
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a(n) = ((9 + sqrt(2))^n + (9 - sqrt(2))^n)/2.
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4
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1, 9, 83, 783, 7537, 73809, 733139, 7365591, 74662657, 762046137, 7818480563, 80531005311, 831898131121, 8612216940609, 89299952572403, 927034007995143, 9631915890692737, 100138799400852969, 1041577033850627219
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OFFSET
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0,2
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COMMENTS
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Hankel transform is := [1, 2, 0, 0, 0, 0, 0, 0, 0, 0, ...]. - Philippe Deléham, Dec 04 2008
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LINKS
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FORMULA
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a(n) = 18*a(n-1) - 79*a(n-2), n > 1; a(0)=1, a(1)=9.
G.f.: (1 - 9*x)/(1 - 18*x + 79*x^2).
a(n) = (Sum_{k=0..n} A098158(n,k)*9^(2k)*2^(n-k))/9^n. (End)
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MATHEMATICA
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LinearRecurrence[{18, -79}, {1, 9}, 50] (* G. C. Greubel, Aug 17 2018 *)
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PROG
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(Magma) Z<x>:= PolynomialRing(Integers()); N<r2>:=NumberField(x^2-2); S:=[ ((9+r2)^n+(9-r2)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 19 2008
(PARI) x='x+O('x^30); Vec((1-9*x)/(1-18*x+79*x^2)) \\ G. C. Greubel, Aug 17 2018
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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), Nov 17 2008
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EXTENSIONS
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STATUS
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approved
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