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A157881
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Expansion of 152*x^2 / (-x^3+1443*x^2-1443*x+1).
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2
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0, 152, 219336, 316282512, 456079163120, 657665836936680, 948353680783529592, 1367525350024012735136, 1971970606380945580536672, 2843580246875973503121146040, 4100440744024547410555112053160, 5912832709303150490046968459510832
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OFFSET
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1,2
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COMMENTS
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This sequence is part of a solution of a more general problem involving two equations, three sequences a(n), b(n), c(n) and a constant A:
A * c(n)+1 = a(n)^2,
(A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
A157881 is the c(n) sequence for A=9.
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LINKS
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FORMULA
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G.f.: 152*x^2/(-x^3+1443*x^2-1443*x+1).
c(1) = 0, c(2) = 152, c(3) = 1443*c(2), c(n) = 1443 * (c(n-1)-c(n-2)) + c(n-3) for n>3.
a(n) = -((721+228*sqrt(10))^(-n)*(-1+(721+228*sqrt(10))^n)*(19+6*sqrt(10)+(-19+6*sqrt(10))*(721+228*sqrt(10))^n))/360. - Colin Barker, Jul 25 2016
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MATHEMATICA
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LinearRecurrence[{1443, -1443, 1}, {0, 152, 219336}, 20] (* Harvey P. Dale, Jul 18 2019 *)
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PROG
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(PARI) a(n) = round(-((721+228*sqrt(10))^(-n)*(-1+(721+228*sqrt(10))^n)*(19+6*sqrt(10)+(-19+6*sqrt(10))*(721+228*sqrt(10))^n))/360) \\ Colin Barker, Jul 25 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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EXTENSIONS
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STATUS
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approved
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