A123381 Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 16*X*Y = 0 with X >= Y.

0, 40, 11664, 3733880, 1201904928, 387002605000, 124613510434992, 40125161088048920, 12920177216118344256, 4160256937698274701160, 1339589813748515664595920, 431343759769849048394285240

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