login
A123381
Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 16*X*Y = 0 with X >= Y.
2
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
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
KEYWORD
nonn
AUTHOR
Mohamed Bouhamida, Oct 13 2006
EXTENSIONS
More terms from Max Alekseyev, Nov 13 2009
STATUS
approved