A071104 Number of perfect matchings in variant of 2n-1 X 2n Aztec rectangle graph.

448, 1018368, 32505856000, 21457409146880000, 217683729041040447897600

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

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 A344827 A345314

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