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%I #19 Sep 08 2022 08:45:41
%S 10081,40897,92449,164737,257761,371521,506017,661249,837217,1033921,
%T 1251361,1489537,1748449,2028097,2328481,2649601,2991457,3354049,
%U 3737377,4141441,4566241,5011777,5478049,5965057,6472801,7001281
%N a(n) = 10368*n^2 - 288*n + 1.
%C The identity (10368*n^2 - 288*n + 1)^2 - (36*n^2 - n)*(1728*n - 24)^2 = 1 can be written as a(n)^2 - A157286(n)*A157287(n)^2 = 1 (see also second part of the comment at A157286). - _Vincenzo Librandi_, Jan 28 2012
%H Vincenzo Librandi, <a href="/A157288/b157288.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 28 2012
%F G.f.: x*(-10081 - 10654*x - x^2)/(x-1)^3. - _Vincenzo Librandi_, Jan 28 2012
%t LinearRecurrence[{3,-3,1},{10081,40897,92449},40] (* _Vincenzo Librandi_, Jan 28 2012 *)
%o (Magma) I:=[10081, 40897, 92449]; [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 28 2012
%o (PARI) for(n=1, 40, print1(10368*n^2 - 288*n + 1", ")); \\ _Vincenzo Librandi_, Jan 28 2012
%Y Cf. A157286, A157287.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 27 2009
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