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%I #14 Feb 20 2018 14:20:53
%S 0,0,6,208,600,3252,10584,27584,61992,125300,233772,409584,682084,
%T 1089172,1678800,2510592,3657584,5208084,7267652,9961200,13435212,
%U 17860084,23432584,30378432,38955000,49454132,62205084
%N Number of ways to place 3 nonattacking knights on an n X n toroidal board.
%H Vincenzo Librandi, <a href="/A172530/b172530.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>
%F a(n) = n^2*(n^4 - 27*n^2 + 218)/6, n>=6.
%F G.f.: -2*x^3 * (50*x^9 -398*x^8 +1425*x^7 -2989*x^6 +3971*x^5 -3325*x^4 +1605*x^3 -365*x^2 +83*x +3) / (x-1)^7. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[- 2 x^2 (50 x^9 - 398 x^8 + 1425 x^7 - 2989 x^6 + 3971 x^5 - 3325 x^4 + 1605 x^3 - 365 x^2 + 83 x + 3) / (x - 1)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 29 2013 *)
%Y Cf. A172529, A172134, A172518.
%K nonn,easy
%O 1,3
%A _Vaclav Kotesovec_, Feb 06 2010
%E More terms from _Vincenzo Librandi_, May 29 2013
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