A372093 -id:A372093 - cp's OEIS frontend

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

Offset: 1

Andrew Howroyd, Jan 12 2018

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.

			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 ...
...

Andrew Howroyd, Table of n, a(n) for n = 1..91
Eric Weisstein's World of Mathematics, Torus Grid Graph

Main diagonal is A054759.
Rows 2..5 are 2*A099754, 2*A170938, A298201, A372093, A372094.
Cf. A212801, A298117.

A372094 Number of Eulerian orientations of the torus grid graph C_6 X C_n.

Original entry on oeis.org

128, 858, 8324, 98466, 1250228, 16448400, 220603364, 2995602834, 41048196236, 566597492178, 7869683384900, 109903205061360, 1542297167382164, 21736984452051810, 307535339926640204, 4365796637993895186, 62162535924592508036, 887421840845709378960

Offset: 1

Brendan McKay, Apr 18 2024

nonn

Brendan McKay, Table of n, a(n) for n = 1..100
Eric Weisstein's World of Mathematics, Torus Grid Graph
Index entries for linear recurrences with constant coefficients, signature (55, -1265, 15974, -121977, 578547, -1629798, 2030265, 2559843, -15001158, 26229897, -19679739, -3755273, 21563768, -20454442, 10081600, -2802792, 410688, -24192).

Row 6 of A298119.

Cf. A298201, A372093.

a(n) = 55*a(n-1) - 1265*a(n-2) + 15974*a(n-3) - 121977*a(n-4) + 578547*a(n-5) - 1629798*a(n-6) + 2030265*a(n-7) + 2559843*a(n-8) - 15001158*a(n-9) + 26229897*a(n-10) - 19679739*a(n-11) - 3755273*a(n-12) + 21563768*a(n-13) - 20454442*a(n-14) + 10081600*a(n-15) - 2802792*a(n-16) + 410688*a(n-17) - 24192*a(n-18)

cp's OEIS Frontend

A298119 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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