A123379 - OEIS

%I #13 May 03 2023 11:57:00

%S 0,20,5832,1866940,600952464,193501302500,62306755217496,

%T 20062580544024460,6460088608059172128,2080128468849137350580,

%U 669794906874257832297960,215671879884924524197142620

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

%C Sequence gives X values. To find Y values: b(n)=c(n)*(-1+d(n))which gives: 0, 16, 5760, 1865648, 600929280, ...

%H G. C. Greubel, <a href="/A123379/b123379.txt">Table of n, a(n) for n = 0..395</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (340,-5798,340,-1).

%F 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).

%F From _Max Alekseyev_, Nov 13 2009: (Start)

%F For n>=4, a(n) = 340*a(n-1) - 5798*a(n-2) + 340*a(n-3) - a(n-4).

%F O.g.f.: 4*x*(5*x^2 -242*x +5)/((x^2 -18*x +1)*(x^2 -322*x +1)) (End)

%t 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 *)

%t LinearRecurrence[{340,-5798,340,-1},{0,20,5832,1866940},20] (* _Harvey P. Dale_, May 03 2023 *)

%o (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

%K nonn

%O 0,2

%A _Mohamed Bouhamida_, Oct 13 2006

%E More terms from _Max Alekseyev_, Nov 13 2009