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Revision History for A071104

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Showing entries 1-10 | older changes

A071104

Number of perfect matchings in variant of 2n-1 X 2n Aztec rectangle graph.
(history; published version)

#11 by N. J. A. Sloane at Mon Mar 07 17:07:13 EST 2016

STATUS

proposed

approved

#10 by Andrew Howroyd at Mon Mar 07 12:02:46 EST 2016

STATUS

editing

proposed

#9 by Andrew Howroyd at Mon Mar 07 11:44:35 EST 2016

DATA

448, 1018368, 32505856000, 21457409146880000, 217683729041040447897600

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

KEYWORD

nonn,brefmore

EXTENSIONS

a(4)-a(5) from Andrew Howroyd, Mar 07 2016

STATUS

approved

editing

Discussion

Mon Mar 07

11:59

Andrew Howroyd: Interest in this graph is/was that terms have many small factors. My thinking is that it may not be too hard to extend this sequence further using the linear algebra method. (as used to compute 60 terms of A039907 - I get to about 25 terms on that sequence which is substantially less. Term 6 on this sequence would require processing a graph with 390 nodes).

#8 by Michael Somos at Sat Apr 25 21:36:09 EDT 2015

STATUS

editing

approved

#7 by Michael Somos at Sat Apr 25 21:35:59 EDT 2015

LINKS

J. Propp, <a href="http://mathfaculty.wiscuml.edu/~proppjpropp/update.ps.gzpdf">Updated article</a>

STATUS

approved

editing

Discussion

Sat Apr 25

21:36

Michael Somos: Updated a PDF

#6 by Russ Cox at Fri Mar 30 16:49:25 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com), _, May 28 2002

Discussion

Fri Mar 30

16:49

OEIS Server: https://oeis.org/edit/global/110

#5 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

KEYWORD

nonn,bref,new

AUTHOR

N. J. A. Sloane (njas, (AT)research.att.com), May 28 2002

#4 by N. J. A. Sloane at Wed Sep 22 03:00:00 EDT 2004

LINKS

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>

KEYWORD

nonn,bref,new

#3 by N. J. A. Sloane at Sat Jun 12 03:00:00 EDT 2004

NAME

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

KEYWORD

nonn,bref,new

#2 by N. J. A. Sloane at Sat Sep 13 03:00:00 EDT 2003

KEYWORD

nonn,newbref