Let 
denote the 
triangular lattice with wraparound. Call an orientation
of 
an assignment of a direction to each edge of 
, and denote the number of orientations of 
such that each vertex has three inwardly directed and three
outwardly directly edges by 
. Such an orientation is said to consist of Eulerian orientation.
Baxter showed that
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
(OEIS A104956; Finch 2003, p. 412), which is known as the twenty-vertex entropy constant (a term coined here for the first time).
Model on a Triangular Lattice." J. Math. Phys. 10,
1211-1216, 1969.Baxter, R. J.