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%I #6 Jun 01 2014 14:38:49
%S 0,0,0,56,1044,6632,26172,78536,196916,434584,871612,1622552,2845076,
%T 4749576,7609724,11773992,17678132,25858616,36967036,51785464,
%U 71242772,96431912,128628156,169308296,220170804,283156952,360472892,454612696,568382356,704924744
%N Number of 3-matchings of the n X n grid graph.
%C Number of ways 3 dominoes can be placed on an n X n chessboard.
%H Alois P. Heinz, <a href="/A243206/b243206.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: 4*x^3*(-14-163*x-125*x^2-5*x^5-6*x^4+72*x^3+x^6)/(x-1)^7.
%F a(n) = (4*n^6-12*n^5-30*n^4+116*n^3+14*n^2-272*n+156)/3 for n>=3, a(n) = 0 for n<3.
%p a:= n-> `if`(n<3, 0, ((((((4*n-12)*n-30)*n+116)*n+14)*n-272)*n+156)/3):
%p seq(a(n), n=0..40);
%Y Column k=3 of A242861.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Jun 01 2014
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