A158317 - OEIS

%I #23 Feb 09 2026 11:53:40

%S 399,799,1199,1599,1999,2399,2799,3199,3599,3999,4399,4799,5199,5599,

%T 5999,6399,6799,7199,7599,7999,8399,8799,9199,9599,9999,10399,10799,

%U 11199,11599,11999,12399,12799,13199,13599,13999,14399,14799,15199

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

%C The identity (400*n-1)^2-(400*n^2-2*n)*(20)^2=1 can be written as a(n)^2-A158316(n)*(20)^2 = 1.

%H Vincenzo Librandi, <a href="/A158317/b158317.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 a(n) = 2*a(n-1)-a(n-2).

%F G.f.: x*(399+x)/(1-x)^2.

%t LinearRecurrence[{2,-1},{399,799},50]

%t 400 Range[40]-1 (* _Harvey P. Dale_, Feb 09 2026 *)

%o (Magma) I:=[399, 799]; [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. A158316.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 16 2009