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%I #15 Sep 12 2015 11:00:26
%S 0,1,78,1278,10002,50191,189208,584958,1563488,3737987,8181786,
%T 16669638,32003238,58438623,102234772,172344406,281269668,446107043,
%U 689807558,1042679982,1544166426,2244921423,3209227248,4517779918
%N Number of ways to place 4 nonattacking grasshoppers on a chessboard of size n x n.
%C The Grasshopper moves on the same lines as a queen, but must jump over a hurdle to land on the square immediately beyond.
%H Vincenzo Librandi, <a href="/A190396/b190396.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, kings, bishops and knights</a> (in English and Czech)
%F a(n) = 1/24*(n^8 -6*n^6 -80*n^5 +431*n^4 -552*n^3 -666*n^2 +2168*n -1392), n>2.
%F G.f.: -x^2*(2*x^9 -22*x^8 +50*x^7 +78*x^6 -89*x^5 -245*x^4 +1224*x^3 +612*x^2 +69*x +1)/(x-1)^9.
%t CoefficientList[Series[- x (2 x^9 - 22 x^8 + 50 x^7 + 78 x^6 - 89 x^5 - 245 x^4 + 1224 x^3 + 612 x^2 + 69 x + 1) / (x - 1)^9, {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 02 2013 *)
%Y Cf.: A190395, A061994.
%K nonn,easy
%O 1,3
%A _Vaclav Kotesovec_, May 10 2011