|
%I #23 Sep 08 2022 08:45:43
%S 840,1681,2522,3363,4204,5045,5886,6727,7568,8409,9250,10091,10932,
%T 11773,12614,13455,14296,15137,15978,16819,17660,18501,19342,20183,
%U 21024,21865,22706,23547,24388,25229,26070,26911,27752,28593,29434
%N a(n) = 841*n - 1.
%C The identity (841*n-1)^2 - (841*n^2-2*n)*(29)^2 = 1 can be written as a(n)^2 - A158401(n)*(29)^2 = 1.
%H Vincenzo Librandi, <a href="/A158402/b158402.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*(29^2*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*(840+x)/(1-x)^2.
%t LinearRecurrence[{2,-1},{840,1681},50]
%t 841 Range[40]-1 (* _Harvey P. Dale_, Jan 29 2011 *)
%o (Magma) I:=[840, 1681]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n) = 841*n - 1.
%Y Cf. A158401.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 18 2009
|
