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A298119
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Array read by antidiagonals: T(m,n) = number of Eulerian orientations of the torus grid graph C_m X C_n.
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8
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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Array begins:
============================================================
m\n| 1 2 3 4 5 6 7
---|--------------------------------------------------------
1 | 4 8 16 32 64 128 256 ...
2 | 8 18 44 114 308 858 2444 ...
3 | 16 44 148 548 2116 8324 33028 ...
4 | 32 114 548 2970 16892 98466 583412 ...
5 | 64 308 2116 16892 143224 1250228 11091536 ...
6 | 128 858 8324 98466 1250228 16448400 220603364 ...
7 | 256 2444 33028 583412 11091536 220603364 4484823396 ...
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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