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%I #13 Apr 18 2024 04:31:58
%S 4,8,8,16,18,16,32,44,44,32,64,114,148,114,64,128,308,548,548,308,128,
%T 256,858,2116,2970,2116,858,256,512,2444,8324,16892,16892,8324,2444,
%U 512,1024,7074,33028,98466,143224,98466,33028,7074
%N Array read by antidiagonals: T(m,n) = number of Eulerian orientations of the torus grid graph C_m X C_n.
%C In other words, the number of orientations of the m X n torus grid graph in which each vertex has equal indegree and outdegree.
%C Values are always even since reversing the orientation of each edge will always result in another Eulerian orientation.
%H Andrew Howroyd, <a href="/A298119/b298119.txt">Table of n, a(n) for n = 1..91</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>
%e Array begins:
%e ============================================================
%e m\n| 1 2 3 4 5 6 7
%e ---|--------------------------------------------------------
%e 1 | 4 8 16 32 64 128 256 ...
%e 2 | 8 18 44 114 308 858 2444 ...
%e 3 | 16 44 148 548 2116 8324 33028 ...
%e 4 | 32 114 548 2970 16892 98466 583412 ...
%e 5 | 64 308 2116 16892 143224 1250228 11091536 ...
%e 6 | 128 858 8324 98466 1250228 16448400 220603364 ...
%e 7 | 256 2444 33028 583412 11091536 220603364 4484823396 ...
%e ...
%Y Main diagonal is A054759.
%Y Rows 2..5 are 2*A099754, 2*A170938, A298201, A372093, A372094.
%Y Cf. A212801, A298117.
%K nonn,tabl
%O 1,1
%A _Andrew Howroyd_, Jan 12 2018
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