A176382 - OEIS

%I #10 Sep 08 2022 08:45:52

%S 1,2281249,10408194000001,47487364308614281249,

%T 216661004683313632776000001,988515400545561595548925838281249,

%U 4510099537958107027564099725673746000001

%N x-values in the solution to x^2-73*y^2=1.

%C The corresponding values of y of this Pell equation are in A176384.

%H Vincenzo Librandi, <a href="/A176382/b176382.txt">Table of n, a(n) for n = 1..150</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4562498,-1).

%F a(n) = 4562498*a(n-1)-a(n-2) with a(1)=1, a(2)=2281249.

%F G.f.: x*(1-2281249*x)/(1-4562498*x+x^2).

%t LinearRecurrence[{4562498,-1},{1,2281249},30]

%o (Magma) I:=[1, 2281249]; [n le 2 select I[n] else 4562498*Self(n-1)-Self(n-2): n in [1..10]];

%Y Cf. A176384.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Apr 16 2010