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A163349
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a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
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2
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1, 9, 67, 463, 3089, 20241, 131363, 848087, 5459521, 35089209, 225323107, 1446179263, 9279361169, 59531488641, 381889579523, 2449671556487, 15713255235841, 100790106559209, 646496195167747, 4146789500815663
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A081180 without initial 0. Fifth binomial transform of A143095.
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LINKS
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FORMULA
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a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
a(n) = ((1+2*sqrt(2))*(5+sqrt(2))^n + (1-2*sqrt(2))*(5-sqrt(2))^n)/2.
G.f.: (1-x)/(1-10*x+23*x^2).
E.g.f.: exp(5*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 19 2016
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MATHEMATICA
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LinearRecurrence[{10, -23}, {1, 9}, 50] (* G. C. Greubel, Dec 19 2016 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+2*r)*(5+r)^n+(1-2*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009
(PARI) Vec((1-x)/(1-10*x+23*x^2) + O(x^50)) \\ G. C. Greubel, Dec 19 2016
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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), Jul 25 2009
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EXTENSIONS
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STATUS
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approved
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