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%I #21 Sep 08 2022 08:45:41
%S 1752,3480,5208,6936,8664,10392,12120,13848,15576,17304,19032,20760,
%T 22488,24216,25944,27672,29400,31128,32856,34584,36312,38040,39768,
%U 41496,43224,44952,46680,48408,50136,51864,53592,55320,57048,58776
%N a(n) = 1728*n + 24.
%C The identity (10368*n^2 + 288*n + 1)^2 - (36*n^2 + n)*(1728*n + 24)^2 = 1 can be written as A157326(n)^2 - A157324(n)*a(n)^2 = 1 (see also second part of the comment at A157324). - _Vincenzo Librandi_, Jan 26 2012
%H Vincenzo Librandi, <a href="/A157325/b157325.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_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: x*(1752 - 24*x)/(1-x)^2. - _Vincenzo Librandi_, Jan 26 2012
%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jan 26 2012
%t LinearRecurrence[{2,-1},{1752,3480},50] (* _Vincenzo Librandi_, Jan 26 2012 *)
%t 1728*Range[40]+24 (* _Harvey P. Dale_, Feb 28 2016 *)
%o (Magma) I:=[1752, 3480]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Jan 26 2012
%o (PARI) for(n=1, 22, print1(1728*n + 24", ")); \\ _Vincenzo Librandi_, Jan 26 2012
%Y Cf. A157324, A157326.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 27 2009
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