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%I #24 Sep 08 2022 08:45:42
%S 486,1940,4362,7752,12110,17436,23730,30992,39222,48420,58586,69720,
%T 81822,94892,108930,123936,139910,156852,174762,193640,213486,234300,
%U 256082,278832,302550,327236,352890,379512,407102,435660,465186,495680
%N a(n) = 484n^2 + 2n.
%C The identity (484*n+1)^2 - (484*n^2 + 2*n)*(22)^2 = 1 can be written as A158326(n)^2 - a(n)*(22)^2 = 1.
%H Vincenzo Librandi, <a href="/A158325/b158325.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&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*(22^2*t+2)).
%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*(486+482*x)/(1-x)^3.
%t LinearRecurrence[{3,-3,1},{486,1940,4362},50]
%o (Magma) I:=[486, 1940, 4362]; [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. A158326.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 16 2009
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