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Number of ways to place 3 non-attacking wazirs on an n X n toroidal board.
8

%I #14 Apr 10 2020 02:13:26

%S 0,0,6,208,1300,4908,14112,34112,73008,142700,259908,447312,734812,

%T 1160908,1774200,2635008,3817112,5409612,7518908,10270800,13812708,

%U 18316012,23978512,31027008,39720000,50350508,63249012,78786512,97377708,119484300,145618408

%N Number of ways to place 3 non-attacking wazirs on an n X n toroidal board.

%C A wazir is a leaper [0,1].

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, p.402

%F a(n) = n^2*(n^4-15*n^2+62)/6, n>=4.

%F G.f.: -2*x^3 * (3*x^7 - 15*x^6 + 25*x^5 - 7*x^4 - 17*x^3 - 15*x^2 + 83*x + 3)/(x-1)^7.

%Y Cf. A172226, A201236, A201238, A201239, A201240, A201241, A201242.

%K nonn

%O 1,3

%A _Vaclav Kotesovec_, Nov 28 2011