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%I #15 Sep 08 2022 08:45:42
%S 363,1448,3255,5784,9035,13008,17703,23120,29259,36120,43703,52008,
%T 61035,70784,81255,92448,104363,117000,130359,144440,159243,174768,
%U 191015,207984,225675,244088,263223,283080,303659,324960,346983,369728
%N 361n^2 + 2n.
%C The identity (361*n+1)^2-(361*n^2+2*n)*(19)^2=1 can be written as A158310(n)^2-a(n)*(19)^2=1.
%H Vincenzo Librandi, <a href="/A158309/b158309.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*(19^2*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*(363+359*x)/(1-x)^3.
%t LinearRecurrence[{3,-3,1},{363,1448,3255},50]
%o (Magma) I:=[363, 1448, 3255]; [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) = 361*n^2 + 2*n.
%Y Cf. A158310.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 16 2009