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 A123379 Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 4*X*Y = 0 with X >= Y. 1
 0, 20, 5832, 1866940, 600952464, 193501302500, 62306755217496, 20062580544024460, 6460088608059172128, 2080128468849137350580, 669794906874257832297960, 215671879884924524197142620 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence gives X values. To find Y values: b(n)=c(n)*(-1+d(n))which gives: 0, 16, 5760, 1865648, 600929280, ... LINKS G. C. Greubel, Table of n, a(n) for n = 0..395 Index entries for linear recurrences with constant coefficients, signature (340,-5798,340,-1). FORMULA a(n) = c(n)*(1+d(n)) with c(0) = 0, c(1) = 2 and c(n) = 18*c(n-1) - c(n-2), d(0) = 1, d(1) = 9 and d(n) = 18*d(n-1) - d(n-2). From Max Alekseyev, Nov 13 2009: (Start) For n>=4, a(n) = 340*a(n-1) - 5798*a(n-2) + 340*a(n-3) - a(n-4). O.g.f.: 4*x*(5*x^2 -242*x +5)/((x^2 -18*x +1)*(x^2 -322*x +1)) (End) MATHEMATICA CoefficientList[Series[4*x*(5*x^2 - 242*x + 5)/(x^2 - 18*x + 1)/(x^2 - 322*x + 1), {x, 0, 50}], x] (* G. C. Greubel, Oct 13 2017 *) LinearRecurrence[{340, -5798, 340, -1}, {0, 20, 5832, 1866940}, 20] (* Harvey P. Dale, May 03 2023 *) PROG (PARI) x='x+O('x^50); concat([0], Vec(4*x*(5*x^2 -242*x +5)/((x^2 -18*x +1)*(x^2 -322*x +1)))) \\ G. C. Greubel, Oct 13 2017 CROSSREFS Sequence in context: A227765 A250020 A088852 * A175015 A135292 A222721 Adjacent sequences: A123376 A123377 A123378 * A123380 A123381 A123382 KEYWORD nonn AUTHOR Mohamed Bouhamida, Oct 13 2006 EXTENSIONS More terms from Max Alekseyev, Nov 13 2009 STATUS approved

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Last modified July 20 18:09 EDT 2024. Contains 374459 sequences. (Running on oeis4.)