A123378 Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 2*X*Y = 0 with X >= Y.

0, 60, 82308, 118528020, 170911244616, 246453665407500, 355386005842019724, 512466373637712510180, 738976155386937410086032, 1065603103601110189318267740, 1536598936416627281801814920340

Offset

0,2

Comments

Sequence gives X values. To find Y values: b(n)=c(n)*(-1+d(n))which gives: 0,54,82080,118519362,...

Links

G. C. Greubel, Table of n, a(n) for n = 0..315

Formula

a(n) = c(n)*(1+d(n)) with c(0) = 0, c(1) = 3 and c(n) = 38*c(n-1) - c(n-2), d(0) = 1, d(1) = 19 and d(n) = 38*d(n-1) - d(n-2).

From Max Alekseyev, Nov 13 2009: (Start)

For n>=4, a(n) = 1480*a(n-1) - 54798*a(n-2) + 1480*a(n-3) - a(n-4).

O.g.f.: 12*x*(5*x^2 -541*x +5)/((x^2 -38*x +1)*(x^2 -1442*x +1)). (End)

Mathematica

CoefficientList[Series[12*x*(5*x^2 - 541*x + 5)/(x^2 - 38*x + 1)/(x^2 - 1442*x + 1), {x, 0, 50}], x] (* G. C. Greubel, Oct 13 2017 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(12*x*(5*x^2 -541*x +5)/((x^2 -38*x +1)*(x^2 -1442*x +1)))) \\ G. C. Greubel, Oct 13 2017

Crossrefs

Sequence in context: A185560 A003788 A222019 * A221692 A265714 A166384

Adjacent sequences: A123375 A123376 A123377 * A123379 A123380 A123381

Keyword

nonn

Author

Mohamed Bouhamida, Oct 13 2006

Extensions

More terms from Max Alekseyev, Nov 13 2009

Status

approved