A123283 X-values of solutions to the equation 3(X-Y)^4 - 8*X*Y = 0 with X >= Y.

0, 12, 1000, 96228, 9411920, 922099452, 90354627000, 8853814445268, 867583293703840, 85014307312378092, 8330534516925125000, 816307368189063783108, 79989791546404858955760

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, 8, 960, 95832, 9408000, 922060648, 90354242880, ...

Links

Harvey P. Dale, Table of n, a(n) for n = 0..502

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)=2 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.: 4*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, 12, 1000, 96228}, 20] (* Harvey P. Dale, Dec 22 2019 *)

Crossrefs

Sequence in context: A079916 A204327 A370313 * A272855 A365571 A265488

Adjacent sequences: A123280 A123281 A123282 * A123284 A123285 A123286

Keyword

nonn,easy

Author

Mohamed Bouhamida, Oct 10 2006

Extensions

More terms from Max Alekseyev, Nov 13 2009

Status

approved