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%I #16 Nov 29 2022 13:13:56
%S 92,4843,16794,35945,62296,95847,136598,184549,239700,302051,371602,
%T 448353,532304,623455,721806,827357,940108,1060059,1187210,1321561,
%U 1463112,1611863,1767814,1930965,2101316,2278867,2463618,2655569
%N 3600n^2 - 6049n + 2541.
%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 A157840(n)^2-a(n)*A157839(n)^2=1.
%H Vincenzo Librandi, <a href="/A157838/b157838.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*(-92-4567*x-2541*x^2)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{92,4843,16794},40]
%t Table[3600n^2-6049n+2541,{n,30}] (* _Harvey P. Dale_, Nov 29 2022 *)
%o (Magma) I:=[92, 4843, 16794]; [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) = 3600*n^2 - 6049*n + 2541.
%Y Cf. A157839, A157840.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 07 2009
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