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A054759 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. 4
4, 18, 148, 2970, 143224, 16448400, 4484823396, 2901094068042, 4448410550095612, 16178049740086515288, 139402641051212392498528, 2849295959501939989625992464, 137950545200232788276834783781648 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The n X n square lattice with wrap around is also called the torus grid graph. - Andrew Howroyd, Jan 11 2018

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 412-416.

Computed by Jennifer Henry in Dec. 1998.

LINKS

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

FORMULA

Elliot Lieb proved that lim_{n->inf} (a(n))^(1/n^2) = (4/3)^(3/2). See A118273.

CROSSREFS

Cf. A118273. Main diagonal of A298119.

Sequence in context: A059837 A220266 A218917 * A286630 A330467 A222766

Adjacent sequences:  A054756 A054757 A054758 * A054760 A054761 A054762

KEYWORD

nonn

AUTHOR

Steven Finch, Apr 25 2000

STATUS

approved

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Last modified June 24 20:32 EDT 2022. Contains 354830 sequences. (Running on oeis4.)