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 A123381 Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 16*X*Y = 0 with X >= Y. 2
 0, 40, 11664, 3733880, 1201904928, 387002605000, 124613510434992, 40125161088048920, 12920177216118344256, 4160256937698274701160, 1339589813748515664595920, 431343759769849048394285240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Corresponding Y values: b(n) = c(n)*(-1 + d(n)) (see Formula section for definitions of c(n) and d(n)), which gives 0, 32, 11520, 3731296, 1201858560, ... LINKS G. C. Greubel, Table of n, a(n) for n = 0..395 FORMULA a(n) = c(n)*(1+d(n)) with c(0) = 0, c(1) = 4 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.: 8*x*(5*x^2 - 242*x + 5)/((x^2 - 18*x + 1)*(x^2 - 322*x + 1)). (End) MATHEMATICA CoefficientList[Series[8*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 *) PROG (PARI) x='x+O('x^50); concat([0], Vec(8*x*(5*x^2 -242*x +5)/((x^2 -18*x +1)*(x^2 -322*x +1)))) \\ G. C. Greubel, Oct 13 2017 CROSSREFS Equals 4*A123377. - Michel Marcus, Oct 14 2017 Sequence in context: A184892 A119525 A309553 * A210347 A221391 A279578 Adjacent sequences: A123378 A123379 A123380 * A123382 A123383 A123384 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 September 25 11:00 EDT 2023. Contains 365644 sequences. (Running on oeis4.)