A123394 Values X satisfying the equation 7(X-Y)^4-8XY=0, where X>=Y.

0, 64, 54000, 48387776, 43449047520, 39017102749504, 35037312017058000, 31463467090220398016, 28254158407188855215040, 25372202786113074403284544, 22784209847768873321556750000

Offset

0,2

Comments

To find Y values: b(n) = c(n)*(-1+d(n)) which gives: 0, 56, 53760, 48380584, 43448832000,...

Links

G. C. Greubel, Table of n, a(n) for n = 0..335

Formula

a(n) = c(n)*(1+d(n)) with c(0) = 0, c(1) = 4 and c(n) = 30*c(n-1) - c(n-2), d(0) = 1, d(1) = 15 and d(n) = 30*d(n-1) - d(n-2).

From Max Alekseyev, Nov 13 2009: (Start)

a(n) = 2*A123393(n)

For n>=4, a(n) = 928*a(n-1) - 26942*a(n-2) + 928*a(n-3) - a(n-4).

O.g.f.: 16*x*(4*x^2 -337*x +4)/((x^2 -30*x +1)*(x^2 -898*x +1)). (End)

Mathematica

CoefficientList[Series[16*x*(4*x^2 - 337*x + 4)/(x^2 - 30*x + 1)/(x^2 - 898*x + 1), {x, 0, 50}], x] (* G. C. Greubel, Oct 13 2017 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(16*x*(4*x^2 -337*x +4)/((x^2 -30*x +1)*(x^2 -898*x +1)))) \\ G. C. Greubel, Oct 13 2017

Crossrefs

Sequence in context: A249076 A334605 A103346 * A069445 A227604 A159677

Adjacent sequences: A123391 A123392 A123393 * A123395 A123396 A123397

Keyword

nonn

Author

Mohamed Bouhamida, Oct 14 2006

Extensions

More terms from Max Alekseyev, Nov 13 2009

Status

approved