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%I #13 Sep 12 2015 11:00:26
%S 0,4,76,516,2172,6860,17904,40796,83976,159732,285220,483604,785316,
%T 1229436,1865192,2753580,3969104,5601636,7758396,10566052,14172940,
%U 18751404,24500256,31647356,40452312,51209300,64250004,79946676
%N Number of ways to place 3 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.
%D Christian Poisson, Echecs et mathematiques, Rex Multiplex 29/1990, p.829
%H Vincenzo Librandi, <a href="/A190395/b190395.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 Explicit formula (C. Poisson, 1990): a(n) = 1/6*(n-1)(n^5 +n^4 -2*n^3 -22*n^2 +76*n -72).
%F G.f.: -4*x^2*(3*x^5 -7*x^4 +4*x^3 +17*x^2 +12*x +1)/(x-1)^7.
%t CoefficientList[Series[-4 x (3 x^5 - 7 x^4 + 4 x^3 + 17 x^2 + 12 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 02 2013 *)
%Y Cf. A047659.
%K nonn,easy
%O 1,2
%A _Vaclav Kotesovec_, May 10 2011
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