%I #20 Sep 08 2022 08:45:43

%S 574,2300,5178,9208,14390,20724,28210,36848,46638,57580,69674,82920,

%T 97318,112868,129570,147424,166430,186588,207898,230360,253974,278740,

%U 304658,331728,359950,389324,419850,451528,484358,518340,553474,589760

%N 576n^2 - 2n.

%C The identity (576*n-1)^2-(576*n^2-2*n)*(24)^2=1 can be written as A158372(n)^2-a(n)*(24)^2=1.

%H Vincenzo Librandi, <a href="/A158371/b158371.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*(24^2*t-2)).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F Contribution from Harvey P. Dale, Nov 06 2011: (Start)

%F G.f.: -2*x*(289*x+287)/(x-1)^3.

%F a(1)=574, a(2)=2300, a(3)=5178, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). (End)

%t Table[576n^2-2n,{n,40}] (* or *) LinearRecurrence[{3,-3,1},{574,2300,5178},40] (* _Harvey P. Dale_, Nov 06 2011 *)

%o (Magma) I:=[574, 2300, 5178]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

%o (PARI) a(n) = 576*n^2 - 2*n.

%Y Cf. A158372.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 17 2009