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 A071104 Number of perfect matchings in variant of 2n-1 X 2n Aztec rectangle graph. 0
 448, 1018368, 32505856000, 21457409146880000, 217683729041040447897600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The graph consists of the vertices (x,y) excluding (0,0) bounded by |x|<=k, |y|<=k, |x+y|<=k and |x-y|<=k+1 where k=2n+1. 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 is odd. The graph is planar and has 8*n^2 + 16*n + 6 vertices. Figure 13 in the J. Propp reference shows the graph for n=1.  - Andrew Howroyd, Mar 07 2016 REFERENCES 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). LINKS J. Propp, Updated article J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics CROSSREFS Sequence in context: A229378 A229370 A174154 * A087700 A107666 A020466 Adjacent sequences:  A071101 A071102 A071103 * A071105 A071106 A071107 KEYWORD nonn,more AUTHOR N. J. A. Sloane, May 28 2002 EXTENSIONS a(4)-a(5) from Andrew Howroyd, Mar 07 2016 STATUS approved

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Last modified October 14 09:25 EDT 2019. Contains 327995 sequences. (Running on oeis4.)