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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. 6
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
Eric Weisstein's World of Mathematics, Torus Grid Graph
EXAMPLE
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 ...
...
CROSSREFS
Main diagonal is A054759.
Rows 2..4 are 2*A099754, 2*A170938, A298201.
Sequence in context: A098354 A354455 A209382 * A089474 A141800 A019197
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jan 12 2018
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)