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Search: id:A007764
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| A007764 |
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Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of an n X n grid. |
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+0
7
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| 1, 2, 12, 184, 8512, 1262816, 575780564, 789360053252, 3266598486981642, 41044208702632496804, 1568758030464750013214100, 182413291514248049241470885236, 64528039343270018963357185158482118
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The length of the path varies.
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 331-339.
D. E. Knuth, personal communication.
Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file. (Science Section).
D. E. Knuth, 'Things A Computer Scientist Rarely Talks About,' CSLI Publications, Stanford, CA, 2001, pages 27-28.
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LINKS
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I. Jensen, Table of n, a(n) for n = 1..19 [from the Jensen link below]
M. Bousquet-Melou, A. J. Guttmann and I. Jensen, Self-avoiding walks crossing a square
S. R. Finch, Self-Avoiding-Walk Connective Constants
I. Jensen, Series Expansions for Self-Avoiding Walks
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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Suppose we start at (0,0) and end at (n-1,n-1). Let U, D, L, R denote steps that are up, down, left, right.
a(2) = 2: UR or RU.
a(3) = 12: UURR, UURDRU, UURDDRUU, URUR, URRU, URDRUU and their reflections in the x=y line.
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CROSSREFS
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Adjacent sequences: A007761 A007762 A007763 this_sequence A007765 A007766 A007767
Sequence in context: A134716 A006023 A039748 this_sequence A015195 A051421 A110105
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KEYWORD
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nonn,nice
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AUTHOR
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David G Radcliffe (adcl008(AT)umn.edu) and D. E. Knuth.
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EXTENSIONS
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Computed to n=11 by John Van Rosendale in 1981, extended to n=12 by D. E. Knuth, Dec 07 1995.
Extended to n=19 by M. Bousquet-Melou, A. J. Guttmann and I. Jensen
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