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%I #22 Sep 08 2022 08:45:42
%S 287,575,863,1151,1439,1727,2015,2303,2591,2879,3167,3455,3743,4031,
%T 4319,4607,4895,5183,5471,5759,6047,6335,6623,6911,7199,7487,7775,
%U 8063,8351,8639,8927,9215,9503,9791,10079,10367,10655,10943,11231,11519
%N 288n - 1.
%C The identity (288*n-1)^2-(144*n^2-n)*(24)^2=1 can be written as a(n)^2-A156635(n)*(24)^2=1.
%H Vincenzo Librandi, <a href="/A157997/b157997.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 E. J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(12^2*t-1)).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 2*a(n-1)-a(n-2).
%F G.f.: x*(287+x)/(1-x)^2.
%t LinearRecurrence[{2,-1},{287,575},50]
%t 288*Range[40]-1 (* _Harvey P. Dale_, Aug 24 2019 *)
%o (Magma) I:=[287, 575]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n) = 288*n - 1.
%Y Cf. A156635.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 11 2009
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