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%I #16 Feb 19 2024 11:23:18
%S 2649601,139478401,483667201,1035216001,1794124801,2760393601,
%T 3934022401,5315011201,6903360001,8699068801,10702137601,12912566401,
%U 15330355201,17955504001,20788012801,23827881601,27075110401,30529699201
%N 103680000n^2 - 174211200n + 73180801.
%C The identity (103680000*n^2-174211200*n+73180801)^2-(3600*n^2-6049*n+2541)*(1728000*n-1451760)^2=1 can be written as a(n)^2-A157838(n)*A157839(n)^2=1.
%H Vincenzo Librandi, <a href="/A157840/b157840.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">X^2-AY^2=1</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F G.f.: x*(-2649601-131529598*x-73180801*x^2)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{2649601,139478401,483667201},40]
%t Table[103680000n^2-174211200n+73180801,{n,20}] (* _Harvey P. Dale_, Feb 19 2024 *)
%o (Magma) I:=[2649601, 139478401, 483667201]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o (PARI) a(n) = 103680000*n^2 - 174211200*n + 73180801.
%Y Cf. A157838, A157839.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 07 2009
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