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%I #19 Sep 08 2022 08:45:43
%S 959,3840,8643,15368,24015,34584,47075,61488,77823,96080,116259,
%T 138360,162383,188328,216195,245984,277695,311328,346883,384360,
%U 423759,465080,508323,553488,600575,649584,700515,753368,808143,864840,923459,984000
%N a(n) = 961*n^2 - 2*n.
%C The identity (961*n-1)^2-(961*n^2-2*n)*(31)^2 = 1 can be written as A158412(n)^2-a(n)*(31)^2 = 1.
%H Vincenzo Librandi, <a href="/A158410/b158410.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*(31^2*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*(-959-963*x)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{959,3840,8643},50]
%t Table[961n^2-2n,{n,40}] (* _Harvey P. Dale_, Aug 29 2022 *)
%o (Magma) I:=[959, 3840, 8643]; [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) = 961*n^2 - 2*n.
%Y Cf. A158412.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 18 2009
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