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A071103 Number of perfect matchings in variant of n X n+2 Aztec rectangle graph. 0
12, 168, 4224, 206848, 20316160, 4053794816, 1651951796224, 1376451119022080, 2342575493674434560, 8125862822063095414784, 57307393009149041432330240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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..11.

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: A282045 A304960 A113380 * A012489 A027772 A099270

Adjacent sequences:  A071100 A071101 A071102 * A071104 A071105 A071106

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 28 2002

EXTENSIONS

a(4) inserted, a(6)-a(11) from Andrew Howroyd, Mar 06 2016

STATUS

approved

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Last modified April 1 04:58 EDT 2020. Contains 333155 sequences. (Running on oeis4.)