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%I #17 Sep 12 2015 11:00:26
%S 0,0,28,1668,29092,252584,1441634,6222996,22004086,66972760,181332416,
%T 446905476,1019470032,2179712872,4410518630,8510498516,15756224370,
%U 28128603736,48622240660,81660504068,133643402268,213660267432
%N Number of ways to place 5 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="/A190397/b190397.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) = 1/120*(n^10 -10*n^8 -200*n^7 +1175*n^6 -1136*n^5 -740*n^4 -30520*n^3 +159624*n^2 -289024*n +179175 -135*(-1)^n), n>3.
%F G.f.: 2x^3*(8*x^12 -60*x^11 +75*x^10 +24*x^9 +441*x^8 -1948*x^7 -893*x^6 +4122*x^5 -8491*x^4 -15988*x^3 -6822*x^2 -694*x -14)/((x-1)^11*(x+1)).
%t CoefficientList[Series[2 x^2 (8 x^12 - 60 x^11 + 75 x^10 + 24 x^9 + 441 x^8 - 1948 x^7 - 893 x^6 + 4122 x^5 - 8491 x^4 - 15988 x^3 - 6822 x^2 - 694 x - 14) / ((x - 1)^11 (x+1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 02 2013 *)
%Y Cf. A190395, A190396, A108792.
%K nonn,easy
%O 1,3
%A _Vaclav Kotesovec_, May 10 2011
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