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%I #30 Oct 29 2022 04:49:27
%S 519420,9503670,18487920,27472170,36456420,45440670,54424920,63409170,
%T 72393420,81377670,90361920,99346170,108330420,117314670,126298920,
%U 135283170,144267420,153251670,162235920,171220170,180204420,189188670
%N a(n) = 8984250*n - 8464830.
%C The identity (1482401250*n^2-2793393900*n+1315947601)^2-(27225*n^2-51302*n+24168)*(8984250*n-8464830)^2=1 can be written as A157804(n)^2-A157802(n)*a(n)^2=1.
%H Vincenzo Librandi, <a href="/A157803/b157803.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F From _Harvey P. Dale_, Nov 01 2011: (Start)
%F a(1) = 519420, a(2)=9503670; for n>2, a(n) = 2*a(n-1) - a(n-2).
%F G.f.: 330*x*(25651*x + 1574)/(x-1)^2. (End)
%t 8984250 Range[30] - 8464830 (* or *) LinearRecurrence[{2, -1}, {519420, 9503670}, 30] (* _Harvey P. Dale_, Nov 01 2011 *)
%o (Magma) I:=[519420, 9503670]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
%o (PARI) a(n) = 8984250*n - 8464830;
%Y Cf. A157802, A157804.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 07 2009
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