A228521 - OEIS

A228521

x-values in the solution to the Pell equation x^2 - 29*y^2 = -1.

%I #15 Nov 18 2024 18:55:54

%S 70,1372210,26898060350,527255777608490,10335267725783560630,

%T 202591917433553577860770,3971206755197249507443252910,

%U 77843594612784567411349065681050,1525890137628596335200014878036689190,29910498399952150749806124227926115821330

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

%H Colin Barker, <a href="/A228521/b228521.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (19602,-1).

%F a(n) = 19602*a(n-1)-a(n-2).

%F G.f.: 70*x*(x+1) / (x^2-19602*x+1).

%t LinearRecurrence[{19602,-1},{70,1372210},20] (* _Harvey P. Dale_, Nov 18 2024 *)

%o (PARI) Vec(70*x*(x+1)/(x^2-19602*x+1) + O(x^100))

%Y Cf. A228522 gives the corresponding y-values.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Aug 24 2013