A270273 Array read by antidiagonals: T(n,m) = number of Hamiltonian cycles in C_n X C_m.

0, 0, 0, 1, 1, 1, 1, 3, 3, 1, 1, 6, 48, 6, 1, 1, 5, 126, 126, 5, 1, 1, 8, 390, 1344, 390, 8, 1, 1, 7, 1014, 2930, 2930, 1014, 7, 1, 1, 10, 2982, 28060, 23580, 28060, 2982, 10, 1, 1, 9, 8094, 55230, 145210, 145210, 55230, 8094, 9, 1

Offset

1,8

Links

Andrew Howroyd, Table of n, a(n) for n = 1..191

Artem M. Karavaev, Hamilton Cycles

Eric Weisstein's World of Mathematics, Hamiltonian Cycle

Eric Weisstein's World of Mathematics, Torus Grid Graph

Formula

T(n,2) = A124349(n) / 2.

Example

The start of the sequence as table:
  0 0    1     1       1        1         1 ...
  0 1    3     6       5        8         7 ...
  1 3   48   126     390     1014      2982 ...
  1 6  126  1344    2930    28060     55230 ...
  1 5  390  2930   23580   145210   1045940 ...
  1 8 1014 28060  145210  3273360  16111928 ...
  1 7 2982 55230 1045940 16111928 257165468 ...
  ...

Crossrefs

Row n=3-5 give: A194952, A216588, A358853.

Main diagonal gives A222199.

Sequence in context: A084546 A288266 A174116 * A026515 A075772 A142157

Adjacent sequences: A270270 A270271 A270272 * A270274 A270275 A270276

Keyword

nonn,tabl

Author

Andrew Howroyd, Mar 14 2016

Status

approved