A158313 - OEIS

%I #21 Sep 08 2022 08:45:42

%S 401,801,1201,1601,2001,2401,2801,3201,3601,4001,4401,4801,5201,5601,

%T 6001,6401,6801,7201,7601,8001,8401,8801,9201,9601,10001,10401,10801,

%U 11201,11601,12001,12401,12801,13201,13601,14001,14401,14801,15201

%N a(n) = 400 * n + 1.

%C The identity (400*n+1)^2-(00*n^2+2*n)*(20)^2=1 can be written as a(n)^2-A158312(n)*(20)^2=1.

%H Vincenzo Librandi, <a href="/A158313/b158313.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;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*(20^2*t+2)).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: x*(401-x)/(1-x)^2.

%F a(n) = 2*a(n-1)-a(n-2).

%t LinearRecurrence[{2,-1},{401,801},50]

%t 400*Range[40]+1 (* _Harvey P. Dale_, Jun 01 2018 *)

%o (Magma) I:=[401, 801]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n) = 400*n + 1

%Y Cf. A158312.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 16 2009