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%I #22 Sep 08 2022 08:45:42
%S 103708801,414777601,933206401,1658995201,2592144001,3732652801,
%T 5080521601,6635750401,8398339201,10368288001,12545596801,14930265601,
%U 17522294401,20321683201,23328432001,26542540801,29964009601,33592838401
%N a(n) = 103680000*n^2 + 28800*n + 1.
%C The identity (103680000*n^2 + 28800*n + 1)^2 - (3600*n^2 + n)*(1728000*n + 240)^2 = 1 can be written as a(n)^2 - A157861(n)*A157862(n)^2 = 1. - _Vincenzo Librandi_, Jan 25 2012
%H Vincenzo Librandi, <a href="/A157863/b157863.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). - _Vincenzo Librandi_, Jan 25 2012
%F G.f.: x*(-x^2 - 103651198*x - 103708801)/(x-1)^3. - _Vincenzo Librandi_, Jan 25 2012
%t LinearRecurrence[{3,-3,1},{103708801,414777601,933206401},40] (* _Vincenzo Librandi_, Jan 25 2012 *)
%t Table[103680000*n^2+28800*n+1,{n,20}] (* _Harvey P. Dale_, May 27 2020 *)
%o (Magma) I:=[103708801, 414777601, 933206401]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Jan 25 2012
%o (PARI) for(n=1, 22, print1(103680000*n^2 + 28800*n + 1", ")); \\ _Vincenzo Librandi_, Jan 25 2012
%Y Cf. A157861, A157862.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 08 2009
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