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%I #20 Feb 27 2024 11:58:24
%S 120,482,1086,1932,3020,4350,5922,7736,9792,12090,14630,17412,20436,
%T 23702,27210,30960,34952,39186,43662,48380,53340,58542,63986,69672,
%U 75600,81770,88182,94836,101732,108870,116250,123872,131736,139842
%N a(n) = 121*n^2 - n.
%C The identity (242*n - 1)^2 - (121*n^2 - n)*22^2 = 1 can be written as A157961(n)^2 - a(n)*22^2 = 1. - _Vincenzo Librandi_, Feb 10 2012
%H Vincenzo Librandi, <a href="/A157960/b157960.txt">Table of n, a(n) for n = 1..10000</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 14 in the first table at p. 85, case d(t) = t*(11^2*t-1)).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F G.f.: x*(-120 - 122*x)/(x-1)^3. - _Vincenzo Librandi_, Feb 10 2012
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 10 2012
%t LinearRecurrence[{3, -3, 1}, {120, 482, 1086}, 50] (* _Vincenzo Librandi_, Feb 10 2012 *)
%o (Magma) I:=[120, 482, 1086]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 10 2012
%o (PARI) for(n=1, 40, print1(121*n^2 - n", ")); \\ _Vincenzo Librandi_, Feb 10 2012
%Y Cf. A157961.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 10 2009
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