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%I #15 Feb 20 2018 14:53:33
%S 0,0,0,228,600,12357,68796,275888,872532,2344025,5580762,12107196,
%T 24392446,46261537,83426400,144157632,240119696,387393921,607715342,
%U 929951100
%N Number of ways to place 4 nonattacking knights on an n X n toroidal board.
%H Vincenzo Librandi, <a href="/A172531/b172531.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^6 - 54*n^4 + 1115*n^2 - 8934)/24, n>=9.
%F G.f.: x^4 * (192*x^13 -1728*x^12 +7452*x^11 -21238*x^10 +46658*x^9 -84582*x^8 +125397*x^7 -144875*x^6 +124920*x^5 -79904*x^4 +39969*x^3 -15165*x^2 +1452*x -228) / (x-1)^9. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[x^3 (192 x^13 - 1728 x^12 + 7452 x^11 - 21238 x^10 + 46658 x^9 - 84582 x^8 + 125397 x^7 - 144875 x^6 + 124920 x^5 - 79904 x^4 + 39969 x^3 - 15165 x^2 + 1452 x - 228) / (x - 1)^9, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 29 2013 *)
%Y Cf. A172529, A172530, A172135, A172519.
%K nonn,easy
%O 1,4
%A _Vaclav Kotesovec_, Feb 06 2010