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%I #6 Jun 01 2014 14:40:50
%S 0,0,0,18,2593,39979,281514,1301950,4618099,13628193,35115244,
%T 81502564,174076485,347418199,655313518,1178436234,2034127639,
%U 3388621645,5472091824,8596923568,13179641449,19766948739,29066362930,41981957974,59655750843,83515296889
%N Number of 4-matchings of the n X n grid graph.
%C Number of ways 4 dominoes can be placed on an n X n chessboard.
%H Alois P. Heinz, <a href="/A243215/b243215.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: -(6*x^9 -14*x^8 -155*x^7 +474*x^6 +1267*x^5 -7976*x^4 +13539*x^3 +17290*x^2 +2431*x +18)*x^3 / (x-1)^9.
%F a(n) = (4*n^8 -16*n^7 -60*n^6 +308*n^5 +171*n^4 -1942*n^3 +872*n^2 +3963*n -3366)/6 for n>=4, a(3) = 18, a(n) = 0 for n<=2.
%p a:= n-> `if`(n<4, [0$3, 18][n+1], ((((((((4*n-16)*n-60)
%p *n+308)*n+171)*n-1942)*n+872)*n+3963)*n-3366)/6):
%p seq(a(n), n=0..40);
%Y Column k=4 of A242861.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Jun 01 2014
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