%I #21 Sep 12 2015 11:00:23
%S 0,0,0,0,0,144,392,896,1620,2800,4356,6624,9464,13328,18000,24064,
%T 31212,40176,50540,63200,77616,94864,114264,137088,162500,191984,
%U 224532,261856,302760,349200,399776,456704,518364,587248,661500,743904,832352,929936,1034280,1148800
%N Number of ways to place 2 nonattacking amazons (superqueens) on an n X n toroidal board.
%C An amazon (superqueen) moves like a queen and a knight.
%H Vincenzo Librandi, <a href="/A178972/b178972.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013
%F a(n) = 1/2*n^2*(n^2 -4*n -9/2 +(-1)^n/2), n>=5.
%F G.f.: 4*x^6*(8*x^6 -7*x^5 -30*x^4 +23*x^3 +44*x^2 -26*x -36)/((x-1)^5*(x+1)^3).
%t CoefficientList[Series[4 x^5 (8 x^6 - 7 x^5 - 30 x^4 + 23 x^3 + 44 x^2 - 26 x - 36) / ((x - 1)^5 (x + 1)^3), {x, 0, 50}], x] (* _Vincenzo Librandi_, May 31 2013 *)
%Y Cf. A172200, A172517.
%K nonn,easy
%O 1,6
%A _Vaclav Kotesovec_, Jan 02 2011