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%I #30 Sep 08 2022 08:45:42
%S 387199,1552321,3495367,6216337,9715231,13992049,19046791,24879457,
%T 31490047,38878561,47044999,55989361,65711647,76211857,87489991,
%U 99546049,112380031,125991937,140381767,155549521,171495199,188218801
%N a(n) = 388962*n^2 - 1764*n + 1.
%C The identity (388962*n^2 - 1764*n + 1)^2 - (441*n^2 - 2*n)*(18522*n - 42)^2 = 1 can be written as a(n)^2 - A157737(n)*A157738(n)^2 = 1. - _Vincenzo Librandi_, Jan 25 2012
%C This is the case s=21 of the identity (2*s^4*n^2 - 4*s^2*n + 1)^2 - (s^2*n^2 - 2*n)*(2*s^3*n - 2*s)^2 = 1. - _Bruno Berselli_, Feb 05 2011
%H Vincenzo Librandi, <a href="/A157739/b157739.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: x*(-387199 - 390724*x - x^2)/(x-1)^3. - _Vincenzo Librandi_, Jan 25 2012
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jan 25 2012
%F a(n) = 2*A158319(n)^2 - 1. - _Bruno Berselli_, Feb 05 2012
%t LinearRecurrence[{3,-3,1},{387199,1552321,3495367},40] (* _Vincenzo Librandi_, Jan 25 2012 *)
%o (Magma) I:=[387199, 1552321, 3495367]; [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(388962*n^2-1764*n+1", ")); \\ _Vincenzo Librandi_, Jan 25 2012
%Y Cf. A157737, A157738, A158319.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 05 2009
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