%I #20 Dec 01 2018 15:04:53
%S 1,1,3,58,280,170985,3037561,35203565096,3263262629905,
%T 580992839261272720,326207195516663381931,811740344447523575023878026,
%U 3011882198082438957330143630563,98662906581850761030365769529236858241,2565014347691062208319404612723752103028288
%N Number of ways the maximal number of domicules can be placed on an n X n square.
%C Number of maximum matchings in the n X n king graph. - _Eric W. Weisstein_, Jun 20 2017
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KingGraph.html">King Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximumIndependentEdgeSet.html">Maximum Independent Edge Set</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/King%27s_graph">King's graph</a>
%F a(n) = A243424(n,floor(n^2/2)).
%e a(2) = 3:
%e +---+ +---+ +---+
%e |o-o| |o o| |o o|
%e | | || || | X |
%e |o-o| |o o| |o o|
%e +---+ +---+ +---+.
%e a(3) = 58:
%e +-----+ +-----+ +-----+
%e |o-o o| |o o o| |o o-o|
%e | || | X || | \ |
%e |o o| |o o o| |o o o|
%e || | | | || / |
%e |o o-o| |o-o | |o o |
%e +-----+ +-----+ +-----+ ... .
%Y Cf. A243511.
%Y Even bisection gives A239273.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jun 05 2014