A123380 Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 8*X*Y = 0 with X >= Y.

0, 120, 164616, 237056040, 341822489232, 492907330815000, 710772011684039448, 1024932747275425020360, 1477952310773874820172064, 2131206207202220378636535480, 3073197872833254563603629840680

Offset

0,2

Comments

Sequence gives X values. To find Y values: b(n)=c(n)*(-1+d(n))which gives: 0, 108, 164160, 237038724, ...

Links

Table of n, a(n) for n=0..10.

Index entries for linear recurrences with constant coefficients, signature (1480,-54798,1480,-1).

Formula

a(n) = c(n)*(1+d(n)) with c(0) = 0, c(1) = 6 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.: 24*x*(5*x^2 -541*x +5)/((x^2 -38*x +1)*(x^2 -1442*x +1)). (End)

Mathematica

CoefficientList[Series[24*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 *)
LinearRecurrence[{1480, -54798, 1480, -1}, {0, 120, 164616, 237056040}, 20] (* Harvey P. Dale, Feb 22 2020 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(24*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: A322917 A184127 A068296 * A172805 A008701 A158043

Adjacent sequences: A123377 A123378 A123379 * A123381 A123382 A123383

Keyword

nonn

Author

Mohamed Bouhamida, Oct 13 2006

Extensions

More terms from Max Alekseyev, Nov 13 2009

Status

approved