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%I #18 Apr 18 2023 09:18:35
%S 782,3132,7050,12536,19590,28212,38402,50160,63486,78380,94842,112872,
%T 132470,153636,176370,200672,226542,253980,282986,313560,345702,
%U 379412,414690,451536,489950,529932,571482,614600,659286,705540,753362,802752
%N a(n) = 784n^2 - 2n.
%C The identity (784*n-1)^2-(784*n^2-2*n)*(28)^2 = 1 can be written as A158399(n)^2-a(n)*(28)^2 = 1.
%H Vincenzo Librandi, <a href="/A158398/b158398.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*(28^2*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*(-782-786*x)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{782,3132,7050},50]
%o (Magma) I:=[782, 3132, 7050]; [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) = 784*n^2 - 2*n.
%Y Cf. A158399.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 18 2009
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