A123393 Values X satisfying the equation 7(X-Y)^4-2XY=0, where X>=Y.

0, 32, 27000, 24193888, 21724523760, 19508551374752, 17518656008529000, 15731733545110199008, 14127079203594427607520, 12686101393056537201642272, 11392104923884436660778375000, 10230097535546797197999395487328, 9186616194816098984491676729411280

Offset

0,2

Comments

To find Y values: b(n) = c(n)*(-1+d(n)) which gives: 0, 28, 26880, 24190292, 21724416000, ...

Links

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

Index entries for linear recurrences with constant coefficients, signature (928,-26942,928,-1).

Formula

a(n) = c(n)*(1+d(n)) with c(0) = 0, c(1) = 2 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)

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

O.g.f.: 8*x*(4*x^2 -337*x +4)/((x^2 -30*x +1)*(x^2 -898*x +1)). (End)

Mathematica

CoefficientList[Series[8*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) my(x='x+O('x^50)); concat([0], Vec(8*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: A227659 A230914 A232596 * A245291 A016937 A074800

Adjacent sequences: A123390 A123391 A123392 * A123394 A123395 A123396

Keyword

nonn,easy

Author

Mohamed Bouhamida, Oct 14 2006

Extensions

More terms from Max Alekseyev, Nov 13 2009

Status

approved