

A071104


Number of perfect matchings in variant of 2n1 X 2n Aztec rectangle graph.


0




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 xy<=k+1 where k=2n+1. Vertices (x1,y1) and (x2,y2) are adjacent iff x1x2=1 and y1=y2 or x1=x2 and y1y2=1 or x1x2=y1y2=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. 255291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 28).


LINKS

Table of n, a(n) for n=1..5.
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



