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, 18, 148, 2970, 143224, 16448400, 4484823396, 2901094068042, 4448410550095612, 16178049740086515288, 139402641051212392498528, 2849295959501939989625992464, 137950545200232788276834783781648, 15844635835975276495290739119895808472

Offset: 1

Author

Steven Finch, Apr 25 2000

Keywords

• nonn

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

• 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

Crossrefs

Cf. A118273, A358177. Main diagonal of A298119.

Formula

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

Extensions

a(14) from Brendan McKay, Apr 18 2024