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A157264 a(n) = 10368*n^2 - 15840*n + 6049.

%I A157264 #21 Nov 18 2024 12:48:55
%S A157264 577,15841,51841,108577,186049,284257,403201,542881,703297,884449,
%T A157264 1086337,1308961,1552321,1816417,2101249,2406817,2733121,3080161,
%U A157264 3447937,3836449,4245697,4675681,5126401,5597857,6090049,6602977
%N A157264 a(n) = 10368*n^2 - 15840*n + 6049.
%C A157264 The identity (10368*n^2-15840*n+6049)^2-(36*n^2-55*n+21)*(1728*n-1320)^2=1 can be written as a(n)^2-A157262(n)*A157263(n)^2=1. - _Vincenzo Librandi_, Jan 27 2012
%H A157264 Vincenzo Librandi, <a href="/A157264/b157264.txt">Table of n, a(n) for n = 1..10000</a>
%H A157264 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;tstart=0">X^2-AY^2=1</a>
%H A157264 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A157264 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jan 27 2012
%F A157264 G.f.: x*(-577-14110*x-6049*x^2)/(x-1)^3. - _Vincenzo Librandi_, Jan 27 2012
%F A157264 E.g.f.: (10368*x^2 - 5472*x + 6049)*exp(x) - 6049. - _G. C. Greubel_, Feb 04 2018
%t A157264 LinearRecurrence[{3,-3,1},{577,15841,51841},40] (* _Vincenzo Librandi_, Jan 27 2012 *)
%t A157264 Table[10368n^2-15840n+6049,{n,30}] (* _Harvey P. Dale_, Nov 18 2024 *)
%o A157264 (Magma) I:=[577, 15841, 51841]; [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 27 2012
%o A157264 (PARI) for(n=1, 40, print1(10368*n^2 - 15840*n + 6049", ")); \\ _Vincenzo Librandi_, Jan 27 2012
%Y A157264 Cf. A157262, A157263.
%K A157264 nonn,easy
%O A157264 1,1
%A A157264 _Vincenzo Librandi_, Feb 26 2009