login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123379 Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 4*X*Y = 0 with X >= Y. 1
0, 20, 5832, 1866940, 600952464, 193501302500, 62306755217496, 20062580544024460, 6460088608059172128, 2080128468849137350580, 669794906874257832297960, 215671879884924524197142620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

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) = 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).

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.: 4*x*(5*x^2 -242*x +5)/((x^2 -18*x +1)*(x^2 -322*x +1)) (End)

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Sequence in context: A227765 A250020 A088852 * A175015 A135292 A222721

Adjacent sequences:  A123376 A123377 A123378 * A123380 A123381 A123382

KEYWORD

nonn

AUTHOR

Mohamed Bouhamida, Oct 13 2006

EXTENSIONS

More terms from Max Alekseyev, Nov 13 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 22 14:15 EDT 2021. Contains 345380 sequences. (Running on oeis4.)