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A157324 a(n) = 36*n^2 + n.

%I A157324 #19 Sep 08 2022 08:45:41
%S A157324 37,146,327,580,905,1302,1771,2312,2925,3610,4367,5196,6097,7070,8115,
%T A157324 9232,10421,11682,13015,14420,15897,17446,19067,20760,22525,24362,
%U A157324 26271,28252,30305,32430,34627,36896,39237,41650,44135,46692,49321,52022
%N A157324 a(n) = 36*n^2 + n.
%C A157324 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 - a(n)*A157325(n)^2 = 1.
%C A157324 This is the case s=6 of the identity (8*n^2*s^4 + 8*n*s^2 + 1)^2 - (n^2*s^2 + n)*(8*n*s^3 + 4*s)^2 = 1. - _Vincenzo Librandi_, Jan 26 2012
%H A157324 Vincenzo Librandi, <a href="/A157324/b157324.txt">Table of n, a(n) for n = 1..10000</a>
%H A157324 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;tstart=0">X^2-AY^2=1</a>
%H A157324 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A157324 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jan 26 2012
%F A157324 G.f.: x*(-37 - 35*x)/(x-1)^3. - _Vincenzo Librandi_, Jan 26 2012
%t A157324 LinearRecurrence[{3,-3,1},{37,146,327},50] (* _Vincenzo Librandi_, Jan 26 2012 *)
%t A157324 Table[36n^2+n,{n,50}] (* _Harvey P. Dale_, Mar 09 2019 *)
%o A157324 (Magma) I:=[37, 146, 327]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Jan 26 2012
%o A157324 (PARI) for(n=1, 40, print1(36*n^2 + n", ")); \\ _Vincenzo Librandi_, Jan 26 2012
%Y A157324 Cf. A157325, A157326.
%K A157324 nonn,easy
%O A157324 1,1
%A A157324 _Vincenzo Librandi_, Feb 27 2009