A334553 Number of Eulerian orientations in the n-Aztec diamond graph.

2, 18, 868, 230274, 338942604, 2779683771636, 127320422237993212, 32620173508191539578106, 46794404527960763380238873820, 376118239460804805511929497668632684, 16947204353591524393183053514633085861818452, 4282329728316057313850583887700885027979305243679508

Offset: 1

Author

Andrew Howroyd, May 22 2020

Keywords

• nonn

Comments

This sequence is based on the same Aztec diamond graph considered in A253107. In particular, it is the grid graph bounded by the eight equations x+y=-2n, x+y=2n, x-y=-2n, x-y=2n, x=1-2n, x=2n-1, y=1-2n, and y=2n-1.

An Eulerian orientation of a graph is an orientation of the edges such that every vertex has in-degree equal to out-degree.

All terms are even since reversing the orientation of every arc in any solution gives another solution.

Examples

			a(2) = 18 because the edges of the graph illustrated below can be oriented in 18 different ways such that every vertex has in-degree equal to out-degree.
          o---o
          |   |
      o---o---o---o
      |   |   |   |
      o---o---o---o
          |   |
          o---o
		

Crossrefs

Cf. A253107.