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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
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
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.)