A123379 Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 4*X*Y = 0 with X >= Y.

0, 20, 5832, 1866940, 600952464, 193501302500, 62306755217496, 20062580544024460, 6460088608059172128, 2080128468849137350580, 669794906874257832297960, 215671879884924524197142620

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