%I #26 Sep 01 2024 00:12:01
%S 482,1932,4350,7736,12090,17412,23702,30960,39186,48380,58542,69672,
%T 81770,94836,108870,123872,139842,156780,174686,193560,213402,234212,
%U 255990,278736,302450,327132,352782,379400,406986,435540,465062,495552
%N a(n) = 484*n^2 - 2*n.
%C The identity (484*n-1)^2-(484*n^2-2*n)*(22)^2=1 can be written as A158330(n)^2-a(n)*(22)^2=1.
%H Vincenzo Librandi, <a href="/A158329/b158329.txt">Table of n, a(n) for n = 1..10000</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*(22^2*t-2)).
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">X^2-AY^2=1</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F G.f.: x*(-482-486*x)/(x-1)^3.
%F E.g.f.: 2*exp(x)*x*(241 + 242*x). - _Stefano Spezia_, Aug 31 2024
%t LinearRecurrence[{3,-3,1},{482,1932,4350},50]
%o (Magma) I:=[482, 1932, 4350]; [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) = 484*n^2 - 2*n
%Y Cf. A158330.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 16 2009