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A157874
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Expansion of 104*x^2 / (-x^3+675*x^2-675*x+1).
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3
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0, 104, 70200, 47314800, 31890105104, 21493883525400, 14486845606014600, 9764112444570315104, 6580997300794786365600, 4435582416623241440099400, 2989575967806763935840630104, 2014969766719342269515144590800, 1358086633192868882889271613569200
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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.
A157874 is the c(n) sequence for A=6.
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LINKS
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FORMULA
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G.f.: 104*x^2 / (-x^3+675*x^2-675*x+1).
c(1) = 0, c(2) = 104, c(3) = 675*c(2), c(n) = 675 * (c(n-1)-c(n-2)) + c(n-3) for n>3.
a(n) = -((337+52*sqrt(42))^(-n)*(-1+(337+52*sqrt(42))^n)*(13+2*sqrt(42)+(-13+2*sqrt(42))*(337+52*sqrt(42))^n))/168. - Colin Barker, Jul 25 2016
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MATHEMATICA
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Rest[CoefficientList[Series[104x^2/(-x^3+675x^2-675x+1), {x, 0, 20}], x]] (* or *) LinearRecurrence[{675, -675, 1}, {0, 104, 70200}, 20] (* Harvey P. Dale, Oct 04 2015 *)
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PROG
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(PARI) a(n) = -round((337+52*sqrt(42))^(-n)*(-1+(337+52*sqrt(42))^n)*(13+2*sqrt(42)+(-13+2*sqrt(42))*(337+52*sqrt(42))^n))/168 \\ 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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