A158310 - OEIS

%I #17 Sep 08 2022 08:45:42

%S 362,723,1084,1445,1806,2167,2528,2889,3250,3611,3972,4333,4694,5055,

%T 5416,5777,6138,6499,6860,7221,7582,7943,8304,8665,9026,9387,9748,

%U 10109,10470,10831,11192,11553,11914,12275,12636,12997,13358,13719,14080

%N 361n + 1.

%C The identity (361*n+1)^2-(361*n^2+2*n)*(19)^2=1 can be written as a(n)^2-A158309(n)*(19)^2=1.

%H Vincenzo Librandi, <a href="/A158310/b158310.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*(19^2*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*(362-x)/(1-x)^2.

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

%t LinearRecurrence[{2,-1},{362,723},50]

%t 361*Range[40]+1 (* _Harvey P. Dale_, Jul 09 2016 *)

%o (Magma) I:=[362, 723]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n) = 361*n + 1.

%Y Cf. A158309.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 16 2009