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Number of matchings in the n X n rook graph K_n X K_n.
9

%I #24 Feb 12 2019 14:55:44

%S 1,7,370,270529,3337807996,855404716021831,5352265402523357926168,

%T 940288991338542314571521981185,

%U 5236753179470435264288904589157765055760,1029720447530443779943631183186535523331685533812231

%N Number of matchings in the n X n rook graph K_n X K_n.

%C K_n X K_n is also called the rook graph or lattice graph.

%H Andrew Howroyd, <a href="/A270228/b270228.txt">Table of n, a(n) for n = 1..16</a>

%H Andrew Howroyd, <a href="/A270228/a270228.cs.txt">C# software related to this sequence</a>

%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/Matching.html">Matching</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Rook%27s_graph">Rook's graph</a>, <a href="https://en.wikipedia.org/wiki/Hosoya_index">Hosoya index</a>

%Y Cf. A270227, A270229, A085537 (Wiener index), A002720 (independent vertex sets), A269561, A028420.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Mar 13 2016