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%I #22 Sep 08 2022 08:45:42
%S 198,788,1770,3144,4910,7068,9618,12560,15894,19620,23738,28248,33150,
%T 38444,44130,50208,56678,63540,70794,78440,86478,94908,103730,112944,
%U 122550,132548,142938,153720,164894,176460,188418,200768,213510,226644
%N a(n) = 196*n^2 + 2*n.
%C The identity (196*n+1)^2-(196*n^2+2*n)*(14)^2=1 can be written as A158223(n)^2-a(n)*(14)^2=1.
%H Vincenzo Librandi, <a href="/A158222/b158222.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*(14^2*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*(-194*x-198)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{198,788,1770},50]
%t Table[196n^2+2n,{n,50}] (* _Harvey P. Dale_, Jul 10 2021 *)
%o (Magma) I:=[198, 788, 1770]; [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) = 196*n^2+2*n.
%Y Cf. A158223.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 14 2009
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