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%I #19 Sep 08 2022 08:45:42
%S 10405,49730,118337,216226,343397,499850,685585,900602,1144901,
%T 1418482,1721345,2053490,2414917,2805626,3225617,3674890,4153445,
%U 4661282,5198401,5764802,6360485,6985450,7639697,8323226,9036037,9778130
%N a(n) = 14641*n^2 - 4598*n + 362.
%C The identity (14641*n^2 - 4598*n + 362)^2 - (121*n^2 - 38*n + 3)*(1331*n - 209)^2 = 1 can be written as a(n)^2 - A157443(n)*A157444(n)^2 = 1. - _Vincenzo Librandi_, Jan 26 2012
%H Vincenzo Librandi, <a href="/A157445/b157445.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 26 2012
%F G.f.: x*(-10405 - 18515*x - 362*x^2)/(x-1)^3. - _Vincenzo Librandi_, Jan 26 2012
%t LinearRecurrence[{3,-3,1},{10405,49730,118337},40] (* _Vincenzo Librandi_, Jan 26 2012 *)
%o (Magma) I:=[10405, 49730, 118337]; [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 26 2012
%o (PARI) for(n=1, 22, print1(14641*n^2 - 4598*n + 362", ")); \\ _Vincenzo Librandi_, Jan 26 2012
%Y Cf. A157443, A157444.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 01 2009
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