A123278 X-values of solutions to the equation 3(X-Y)^4 - 2*X*Y = 0 with X >= Y.

0, 6, 500, 48114, 4705960, 461049726, 45177313500, 4426907222634, 433791646851920, 42507153656189046, 4165267258462562500, 408153684094531891554, 39994895773202429477880, 3919091632081792366665966, 384030985048163740834371500, 37631117443087185673897862874

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, 4, 480, 47916, 4704000, 461030324, 45177121440, ...

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (108,-982,108,-1).

Formula

a(n) = c(n)*(1+d(n)) with c(0)=0, c(1)=1 and c(n) = 10*c(n-1) - c(n-2); d(0)=1, d (1)=5 and d(n) = 10*d(n-1) - d(n-2).

For n >= 4, a(n) = 108*a(n-1) - 982*a(n-2) + 108*a(n-3) - a(n-4). - Max Alekseyev, Nov 13 2009

G.f.: 2*x*(3*x^2 - 74*x + 3)/((x^2 - 98*x + 1)*(x^2 - 10*x + 1)). - Colin Barker, Oct 25 2012

Mathematica

LinearRecurrence[{108, -982, 108, -1}, {0, 6, 500, 48114}, 20] (* Harvey P. Dale, Aug 19 2012 *)

Crossrefs

Sequence in context: A197205 A197803 A099057 * A127605 A278775 A013975

Adjacent sequences: A123275 A123276 A123277 * A123279 A123280 A123281

Keyword

nonn,easy

Author

Mohamed Bouhamida, Oct 10 2006

Extensions

More terms from Max Alekseyev, Nov 13 2009

More terms from Harvey P. Dale, Aug 19 2012

Status

approved