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%I #11 Mar 07 2016 17:07:13
%S 448,1018368,32505856000,21457409146880000,217683729041040447897600
%N Number of perfect matchings in variant of 2n-1 X 2n Aztec rectangle graph.
%C 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
%D 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).
%H J. Propp, <a href="http://faculty.uml.edu/jpropp/update.pdf">Updated article</a>
%H J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), <a href="http://www.msri.org/publications/books/Book38/contents.html">New Perspectives in Algebraic Combinatorics</a>
%K nonn,more
%O 1,1
%A _N. J. A. Sloane_, May 28 2002
%E a(4)-a(5) from _Andrew Howroyd_, Mar 07 2016