%I #18 Sep 08 2022 08:45:42
%S 195,391,587,783,979,1175,1371,1567,1763,1959,2155,2351,2547,2743,
%T 2939,3135,3331,3527,3723,3919,4115,4311,4507,4703,4899,5095,5291,
%U 5487,5683,5879,6075,6271,6467,6663,6859,7055,7251,7447,7643,7839,8035,8231,8427
%N 196n - 1.
%C The identity (196*n-1)^2-(196*n^2-2*n)*(14)^2=1 can be written as a(n)^2-A158224(n)*(14)^2=1.
%H Vincenzo Librandi, <a href="/A158225/b158225.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*(14^2*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*(195+x)/(1-x)^2.
%t 196Range[60]-1 (* _Harvey P. Dale_, Mar 23 2011 *)
%t LinearRecurrence[{2,-1},{195,391},50]
%o (Magma) I:=[195, 391]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n) = 196*n - 1.
%Y Cf. A158224.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 14 2009
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