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A157879
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Expansion of 120*x^2 / (-x^3+899*x^2-899*x+1).
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5
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0, 120, 107880, 96876240, 86994755760, 78121193796360, 70152745034375640, 62997086919675528480, 56571313901123590199520, 50800976886122064323640600, 45619220672423712639039059400, 40966009362859607827792751700720, 36787430788627255405645251988187280
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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 2 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.
A157879 is the c(n) sequence for A=7.
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LINKS
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FORMULA
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G.f.: 120*x^2/(-x^3+899*x^2-899*x+1).
c(1) = 0, c(2) = 120, c(3) = 899*c(2), c(n) = 899 * (c(n-1)-c(n-2)) + c(n-3) for n>3.
a(n) = -((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224. - Colin Barker, Jul 25 2016
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MATHEMATICA
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CoefficientList[Series[120x^2/(-x^3+899x^2-899x+1), {x, 0, 30}], x] (* or *) LinearRecurrence[{899, -899, 1}, {0, 0, 120}, 30] (* Harvey P. Dale, Jan 14 2014 *)
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PROG
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(PARI) a(n) = round(-((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224) \\ 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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