A123397 Values X satisfying the equation 9(X-Y)^4-2XY=0, where X>=Y.

0, 36, 39304, 45280620, 52251208976, 60297761989044, 69583562098521240, 80299370262508107516, 92665403695926847089184, 106935795565612276500481860, 123403815417308895154020255656

Offset

0,2

Comments

To find Y values: b(n) = c(n)*(-1+d(n)) which gives: 0, 32, 39168, 45276000, 52251052032, ...

Links

G. C. Greubel, Table of n, a(n) for n = 0..325

Formula

a(n) = c(n)*(1+d(n)) with c(0) = 0, c(1) = 2 and c(n) = 34*c(n-1) - c(n-2), d(0) = 1, d(1) = 17 and d(n) = 34*d(n-1) - d(n-2).

From Max Alekseyev, Nov 13 2009: (Start)

For n>=4, a(n) = 1188*a(n-1) - 39238*a(n-2) + 1188*a(n-3) - a(n-4).

O.g.f.: 4*x*(9*x^2 -866*x +9)/((x^2 -34*x +1)*(x^2 -1154*x +1)). (End)

Mathematica

CoefficientList[Series[4*x*(9*x^2 - 866*x + 9)/(x^2 - 34*x + 1)/(x^2 - 1154*x + 1), {x, 0, 50}], x] (* G. C. Greubel, Oct 13 2017 *)

Prog

(PARI) my(x='x+O('x^50)); concat([0], Vec(4*x*(9*x^2 -866*x +9)/((x^2 -34*x +1)*(x^2 -1154*x +1)))) \\ G. C. Greubel, Oct 13 2017

Crossrefs

Sequence in context: A159431 A028454 A159435 * A185097 A023111 A295927

Adjacent sequences: A123394 A123395 A123396 * A123398 A123399 A123400

Keyword

nonn

Author

Mohamed Bouhamida, Oct 14 2006

Extensions

More terms from Max Alekseyev, Nov 13 2009

Status

approved