%I #15 Feb 20 2018 15:02:29
%S 0,0,6,240,1010,4056,12068,30000,65628,130480,240856,418968,694200,
%T 1104488,1697820,2533856,3685668,5241600,7307248,10007560,13489056,
%U 17922168,23503700,30459408,39046700,49557456,62320968,77707000,96128968,118047240,143972556
%N Number of ways to place 3 nonattacking knights on an n X n cylindrical board.
%H Vincenzo Librandi, <a href="/A172965/b172965.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*(n - 3)(n^4 + 3*n^3 - 18*n^2 - 18*n + 164)/6, n>=6.
%F G.f.: -2*x^3*(15*x^9-141*x^8+564*x^7-1276*x^6+1812*x^5-1652*x^4+908*x^3-272*x^2+99*x+3)/(x-1)^7. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[- 2 x^2 (15 x^9 - 141 x^8 + 564 x^7 - 1276 x^6 + 1812 x^5 - 1652 x^4 + 908 x^3 - 272 x^2 + 99 x + 3) / (x - 1)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 29 2013 *)
%Y Cf. A172530, A172134, A172964.
%K nonn,easy
%O 1,3
%A _Vaclav Kotesovec_, Feb 06 2010
%E More terms from _Vincenzo Librandi_, May 29 2013