

A334553


Number of Eulerian orientations in the nAztec diamond graph.


0



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

1,1


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, xy=2n, xy=2n, x=12n, x=2n1, y=12n, and y=2n1.
An Eulerian orientation of a graph is an orientation of the edges such that every vertex has indegree equal to outdegree.
All terms are even since reversing the orientation of every arc in any solution gives another solution.


LINKS

Table of n, a(n) for n=1..12.


EXAMPLE

a(2) = 18 because the edges of the graph illustrated below can be oriented in 18 different ways such that every vertex has indegree equal to outdegree.
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CROSSREFS

Cf. A253107.
Sequence in context: A306789 A015190 A180606 * A013040 A268051 A268074
Adjacent sequences: A334550 A334551 A334552 * A334554 A334555 A334556


KEYWORD

nonn


AUTHOR

Andrew Howroyd, May 22 2020


STATUS

approved



