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A054344
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Number of ways of covering a 2n x 2n lattice by 2n^2 dominoes with exactly 6 horizontal (or vertical) dominoes.
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2
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9, 1064, 21656, 197484, 1143366, 4927524, 17240292, 51631617, 137044523, 330284988, 735542444, 1533609350, 3024043008, 5684167992, 10249533240, 17821214019, 30006185613, 49097892704, 78305096016
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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REFERENCES
| M. E. Fisher, Statistical mechanics of dimers on a plane lattice, Physical Review, 124 (1961), 1664-1672.
P. W. Kasteleyn, The statistics of dimers on a lattice, Physica, 27 (1961), 1209-1225.
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LINKS
| Index entries for sequences related to dominoes
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FORMULA
| a(n) = (1/720)*n*(n+1)*(120*n^7-300*n^6-70*n^5+363*n^4+416*n^3-231*n^2-394*n-264)
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EXAMPLE
| a(3) = 1064 because we have 1064 ways to cover a 36 x 36 lattice with exactly 6 horizontal (or vertical) dominoes and exactly 12 vertical (or horizontal) dominoes.
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CROSSREFS
| Cf. A004003, A002414, A038758.
Sequence in context: A099127 A172944 A174636 * A048912 A036411 A075412
Adjacent sequences: A054341 A054342 A054343 * A054345 A054346 A054347
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KEYWORD
| nonn
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AUTHOR
| Yong Kong (ykong(AT)curagen.com), May 06 2000
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