A298119 - OEIS

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A298119

Array read by antidiagonals: T(m,n) = number of Eulerian orientations of the torus grid graph C_m X C_n.

4, 8, 8, 16, 18, 16, 32, 44, 44, 32, 64, 114, 148, 114, 64, 128, 308, 548, 548, 308, 128, 256, 858, 2116, 2970, 2116, 858, 256, 512, 2444, 8324, 16892, 16892, 8324, 2444, 512, 1024, 7074, 33028, 98466, 143224, 98466, 33028, 7074

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

In other words, the number of orientations of the m X n torus grid graph in which each vertex has equal indegree and outdegree.

Values are always even since reversing the orientation of each edge will always result in another Eulerian orientation.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..91

Eric Weisstein's World of Mathematics, Torus Grid Graph

EXAMPLE

Array begins:

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