login
Array read by antidiagonals: T(m,n) = number of Eulerian cycles in the torus grid graph C_m X C_n.
7

%I #12 Jan 14 2018 18:19:19

%S 2,4,4,8,40,8,16,320,320,16,32,2368,8616,2368,32,64,16832,207496,

%T 207496,16832,64,128,116608,4788808,15639936,4788808,116608,128,256,

%U 793088,108326760,1116199200,1116199200,108326760,793088,256

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

%H Andrew Howroyd, <a href="/A298117/b298117.txt">Table of n, a(n) for n = 1..105</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EulerianCycle.html">Eulerian Cycle</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

%e ---|---------------------------------------------------------------------

%e 1 | 2 4 8 16 32 64 ...

%e 2 | 4 40 320 2368 16832 116608 ...

%e 3 | 8 320 8616 207496 4788808 108326760 ...

%e 4 | 16 2368 207496 15639936 1116199200 77643032832 ...

%e 5 | 32 16832 4788808 1116199200 242230440480 50917973008584 ...

%e 6 | 64 116608 108326760 77643032832 50917973008584 32098460087825856 ...

%e ...

%Y Rows 2..4 are A298198, A282621, A298197.

%Y Main diagonal is A297385.

%Y Cf. A212801, A298119.

%K nonn,tabl

%O 1,1

%A _Andrew Howroyd_, Jan 12 2018