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%I #19 Feb 27 2023 11:59:46
%S 224,449,674,899,1124,1349,1574,1799,2024,2249,2474,2699,2924,3149,
%T 3374,3599,3824,4049,4274,4499,4724,4949,5174,5399,5624,5849,6074,
%U 6299,6524,6749,6974,7199,7424,7649,7874,8099,8324,8549,8774,8999,9224,9449,9674
%N a(n) = 225*n - 1.
%C The identity (225*n-1)^2-(225*n^2-2*n)*(15)^2=1 can be written as a(n)^2-A158226(n)*(15)^2=1.
%H Vincenzo Librandi, <a href="/A158227/b158227.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 15 in the first table at p. 85, case d(t) = t*(15^2*t-2)).
%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*(224+x)/(1-x)^2.
%t LinearRecurrence[{2,-1},{224,449},50]
%t 225*Range[50]-1 (* _Harvey P. Dale_, Feb 27 2023 *)
%o (Magma) I:=[224, 449]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n) = 225*n - 1.
%Y Cf. A158226.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 14 2009
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