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%I #27 Sep 08 2022 08:45:40
%S 228,444,660,876,1092,1308,1524,1740,1956,2172,2388,2604,2820,3036,
%T 3252,3468,3684,3900,4116,4332,4548,4764,4980,5196,5412,5628,5844,
%U 6060,6276,6492,6708,6924,7140,7356,7572,7788,8004,8220,8436,8652
%N a(n) = 216*n + 12.
%C The identity (648*n^2 + 72*n + 1)^2 - (9*n^2 + n)*(216*n + 12)^2 = 1 can be written as A154515(n)^2 - A154517(n)*a(n)^2 = 1 (see also the second comment at A154515).
%H Vincenzo Librandi, <a href="/A154519/b154519.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: x*(228 - 12*x)/(x-1)^2. - _Vincenzo Librandi_, Jan 30 2012 [corrected by _Georg Fischer_, May 12 2019]
%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jan 30 2012
%F a(n) = 12*A161705(n). - _Michel Marcus_, Aug 19 2018
%t LinearRecurrence[{2, -1}, {228, 444}, 50] (* _Vincenzo Librandi_, Jan 30 2012 *)
%o (PARI) a(n)=216*n+12 \\ _Charles R Greathouse IV_, Dec 27 2011
%o (Magma) I:=[228, 444]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jan 30 2012
%Y Cf. A154515, A154517, A161705.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Jan 11 2009