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%I #17 Sep 08 2022 08:45:43
%S 678,2708,6090,10824,16910,24348,33138,43280,54774,67620,81818,97368,
%T 114270,132524,152130,173088,195398,219060,244074,270440,298158,
%U 327228,357650,389424,422550,457028,492858,530040,568574,608460,649698,692288
%N a(n) = 676*n^2 + 2*n.
%C The identity (676*n+1)^2-(676*n^2+2*n)*(26)^2=1 can be written as A158386(n)^2-a(n)*(26)^2=1.
%H Vincenzo Librandi, <a href="/A158385/b158385.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*(26^2*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*(678+674*x)/(1-x)^3.
%t LinearRecurrence[{3,-3,1},{678,2708,6090},50]
%o (Magma) I:=[678, 2708, 6090]; [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) = 676*n^2 + 2*n.
%Y Cf. A158386.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 17 2009
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