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Number of ways the maximal number of domicules can be placed on an n X n square.
3

%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