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A054759
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Number of Eulerian orientations of the n X n square lattice (with wrap-around), i.e., number of arrow configurations on n X n grid that satisfy the square ice rule.
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4
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4, 18, 148, 2970, 143224, 16448400, 4484823396, 2901094068042, 4448410550095612, 16178049740086515288, 139402641051212392498528, 2849295959501939989625992464, 137950545200232788276834783781648
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OFFSET
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1,1
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COMMENTS
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The n X n square lattice with wrap around is also called the torus grid graph. - Andrew Howroyd, Jan 11 2018
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 412-416.
Computed by Jennifer Henry in Dec. 1998.
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LINKS
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Table of n, a(n) for n=1..13.
E. H. Lieb, Residual entropy of square ice, Phys. Rev. 162 (1967) 162-172.
Steven R. Finch, Lieb's Square Ice Constant [Broken link]
Steven R. Finch, Lieb's Square Ice Constant [From the Wayback machine]
Eric Weisstein's World of Mathematics, Torus Grid Graph
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FORMULA
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Elliot Lieb proved that lim_{n->inf} (a(n))^(1/n^2) = (4/3)^(3/2). See A118273.
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CROSSREFS
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Cf. A118273. Main diagonal of A298119.
Sequence in context: A059837 A220266 A218917 * A286630 A330467 A222766
Adjacent sequences: A054756 A054757 A054758 * A054760 A054761 A054762
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KEYWORD
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nonn
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AUTHOR
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Steven Finch, Apr 25 2000
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STATUS
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approved
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