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A071103
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Number of perfect matchings in variant of n X n+2 Aztec rectangle graph.
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0
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12, 168, 4224, 206848, 20316160, 4053794816, 1651951796224, 1376451119022080, 2342575493674434560, 8125862822063095414784, 57307393009149041432330240
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OFFSET
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1,1
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COMMENTS
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The graph consists of the vertices (x,y) bounded by 0<=x<=2n+1, 0<=y<=2n+1, n+1<=x+y<=3n+1 and |y-x|<=n+2. Vertices (x1,y1) and (x2,y2) are adjacent iff |x1-x2|=1 and y1=y2 or x1=x2 and |y1-y2|=1 or |x1-x2|=|y1-y2|=1 and x1+y1+n is odd. The graph is planar, has A090288(n) vertices and 6*n^2 + 12*n + 1 edges. Figure 12 in the J. Propp reference shows the graph for n=3. - Andrew Howroyd, Mar 06 2016
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REFERENCES
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J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 28).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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