A123268 X-values of solutions to the equation 3(X-Y)^4 - X*Y = 0 with X >= Y.

0, 8, 1372, 263640, 51109688, 9914526952, 1923360309780, 373121890730168, 72383722120389232, 14042068951066270920, 2724088992528477983948, 528459222478004446530712, 102518365071690621381979560

Offset

0,2

Comments

To find Y-values: with c(n) and d(n) as defined in the Formula section, b(n) = c(n)*(-1+d(n)), which gives 0, 6, 1344, 263250, 51104256, 9914451294, ...

Links

Table of n, a(n) for n=0..12.

Index entries for linear recurrences with constant coefficients, signature (208,-2718,208,-1).

Formula

a(n) = c(n)*(1+d(n)) with c(0)=0, c(1)=1 and c(n) = 14*c(n-1) - c(n-2); d(0)=1, d(1)=7 and d(n) = 14*d(n-1) - d(n-2).

For n >= 4, a(n) = 208*a(n-1) - 2718*a(n-2) + 208*a(n-3) - a(n-4). - Max Alekseyev, Nov 13 2009

G.f.: 4*x*(2*x^2 - 73*x + 2)/((x^2 - 194*x + 1)*(x^2 - 14*x + 1)). - Colin Barker, Oct 25 2012

Crossrefs

Sequence in context: A270112 A281127 A001418 * A088080 A230472 A160103

Adjacent sequences: A123265 A123266 A123267 * A123269 A123270 A123271

Keyword

nonn,easy

Author

Mohamed Bouhamida, Oct 09 2006

Extensions

More terms from Max Alekseyev, Nov 13 2009

Status

approved