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Number of ways to place 2 nonattacking knights on an n X n toroidal board.
7

%I #13 Feb 20 2018 14:53:20

%S 0,2,18,88,200,486,980,1760,2916,4550,6776,9720,13520,18326,24300,

%T 31616,40460,51030,63536,78200,95256,114950,137540,163296,192500,

%U 225446,262440,303800,349856,400950,457436,519680,588060,662966,744800,833976,930920,1036070

%N Number of ways to place 2 nonattacking knights on an n X n toroidal board.

%H Vincenzo Librandi, <a href="/A172529/b172529.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+3)*(n-3)/2, n>=5.

%F G.f.: 2*x^2*(16*x^7-71*x^6+121*x^5-98*x^4+40*x^3-9*x^2-4*x-1)/(x-1)^5. - _Vaclav Kotesovec_, Mar 25 2010

%t CoefficientList[Series[2 x (16 x^7 - 71 x^6 + 121 x^5 - 98 x^4 + 40 x^3 - 9 x^2 - 4 x - 1) / (x - 1)^5, {x, 0, 50}], x] ( * _Vincenzo Librandi_, May 29 2013 *)

%Y Cf. A172132, A172517.

%K nonn,easy

%O 1,2

%A _Vaclav Kotesovec_, Feb 06 2010

%E More terms from _Vincenzo Librandi_, May 29 2013