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

%I #17 Feb 15 2020 10:52:26

%S 0,6,500,48114,4705960,461049726,45177313500,4426907222634,

%T 433791646851920,42507153656189046,4165267258462562500,

%U 408153684094531891554,39994895773202429477880,3919091632081792366665966,384030985048163740834371500,37631117443087185673897862874

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

%C 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, ...

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (108,-982,108,-1).

%F 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).

%F 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

%F 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

%t LinearRecurrence[{108,-982,108,-1},{0,6,500,48114},20] (* _Harvey P. Dale_, Aug 19 2012 *)

%K nonn,easy

%O 0,2

%A _Mohamed Bouhamida_, Oct 10 2006

%E More terms from _Max Alekseyev_, Nov 13 2009

%E More terms from _Harvey P. Dale_, Aug 19 2012

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)