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%I #20 Sep 08 2022 08:45:42
%S 142,572,1290,2296,3590,5172,7042,9200,11646,14380,17402,20712,24310,
%T 28196,32370,36832,41582,46620,51946,57560,63462,69652,76130,82896,
%U 89950,97292,104922,112840,121046,129540,138322,147392,156750,166396
%N a(n) = 144*n^2 - 2*n.
%C The identity (144*n - 1)^2 - (144*n^2 - 2*n)*12^2 = 1 can be written as A158136(n)^2 - a(n)*12^2 = 1. - _Vincenzo Librandi_, Feb 11 2012
%H Vincenzo Librandi, <a href="/A158135/b158135.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 15 in the first table at p. 85, case d(t) = t*(12^2*t-2)).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: x*(-142 - 146*x)/(x-1)^3. - _Vincenzo Librandi_, Feb 11 2012
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 11 2012
%t LinearRecurrence[{3, -3, 1}, {142, 572, 1290}, 50] (* _Vincenzo Librandi_, Feb 11 2012 *)
%o (Magma) I:=[142, 572, 1290]; [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 11 2012
%o (PARI) for(n=1, 50, print1(144*n^2 - 2*n", ")); \\ _Vincenzo Librandi_, Feb 11 2012
%Y Cf. A158136.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 13 2009
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