A174770 - OEIS

%I #16 Sep 08 2022 08:45:51

%S 0,1820,35675640,699313893460,13707950903927280,268703252919468649100,

%T 5267121150019473555730920,103246108513978467719968844740,

%U 2023830213823884774227355738862560

%N y-values in the solution to x^2 - 29*y^2 = 1.

%C The corresponding values of x of this Pell equation are in A174769.

%H Vincenzo Librandi, <a href="/A174770/b174770.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (19602,-1).

%F a(n) = 19602*a(n-1)-a(n-2) with a(1)=0, a(2)=1820.

%F G.f.: 1820*x^2/(1-19602*x+x^2).

%t LinearRecurrence[{19602,-1}, {0,1820}, 30]

%t Table[-((9801-1820*Sqrt[29])^x-(9801+1820*Sqrt[29])^x)/(2*Sqrt[29]),{x,0,10}]// Simplify (* _Harvey P. Dale_, Jul 02 2022 *)

%o (Magma) I:=[0, 1820]; [n le 2 select I[n] else 19602*Self(n-1)-Self(n-2): n in [1..20]];

%Y Cf. A174769.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Apr 14 2010