%I #12 Feb 11 2024 09:15:38

%S 0,1,52,2703,140504,7303505,379641756,19734067807,1025791884208,

%T 53321443911009,2771689291488260,144074521713478511,

%U 7489103439809394312,389289304348375025713,20235554722675691942764,1051859556274787605998015,54676461371566279819954016,2842124131765171763031610817

%N a(n) = sqrt((A114052(n)^2 - 1)/27)/5.

%C 5*a(n) are the y-values in solutions to x^2 - 27*y^2 = 1.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (52,-1).

%F G.f.: x/(1 - 52*x + x^2).

%e a(2) = 52: A114052(2) = 1351; 1351^2 - 27*(5*52)^2 = 1825201 - 1825200 = 1.

%t LinearRecurrence[{52, -1}, {0, 1}, 18]

%Y Cf. A114052.

%K nonn,easy

%O 0,3

%A _Hugo Pfoertner_, Feb 11 2024