%I #21 Sep 08 2022 08:45:42
%S 161,323,485,647,809,971,1133,1295,1457,1619,1781,1943,2105,2267,2429,
%T 2591,2753,2915,3077,3239,3401,3563,3725,3887,4049,4211,4373,4535,
%U 4697,4859,5021,5183,5345,5507,5669,5831,5993,6155,6317,6479,6641,6803,6965
%N 162n - 1.
%C The identity (162*n-1)^2-(81*n^2-n)*(18)^2=1 can be written as a(n)^2-A157953(n)*(16)^2=1. - _Vincenzo Librandi_, Jan 29 2012
%H Vincenzo Librandi, <a href="/A157954/b157954.txt">Table of n, a(n) for n = 1..10000</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*(9^2*t-1)).
%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_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 2*a(n-1)-a(n-2). - _Vincenzo Librandi_, Jan 29 2012
%F G.f.: x*(161+x)/(1-x)^2. - _Vincenzo Librandi_, Jan 29 2012
%p A157954:=n->162*n - 1; seq(A157954(n), n=1..50); # _Wesley Ivan Hurt_, Mar 06 2014
%t LinearRecurrence[{2,-1},{161,323},50] (* _Vincenzo Librandi_, Jan 29 2012 *)
%o (Magma) I:=[161, 323]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jan 29 2012
%o (PARI) for(n=1, 40, print1(162*n - 1", ")); \\ _Vincenzo Librandi_, Jan 29 2012
%Y Cf. A157953.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 10 2009