A350729 Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n king graph.

1, 1, 1, 1, 12, 1, 1, 48, 48, 1, 1, 208, 392, 208, 1, 1, 768, 4678, 4678, 768, 1, 1, 2752, 43676, 171592, 43676, 2752, 1, 1, 9472, 406396, 4743130, 4743130, 406396, 9472, 1, 1, 32000, 3568906, 132202038, 364618672, 132202038, 3568906, 32000, 1

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..231

Eric Weisstein's World of Mathematics, Hamiltonian Path

Eric Weisstein's World of Mathematics, King Graph

Formula

T(m,n) = T(n,m).

Example

Array begins:
===========================================================
m\n | 1    2      3         4           5             6 ...
----+------------------------------------------------------
  1 | 1    1      1         1           1             1 ...
  2 | 1   12     48       208         768          2752 ...
  3 | 1   48    392      4678       43676        406396 ...
  4 | 1  208   4678    171592     4743130     132202038 ...
  5 | 1  768  43676   4743130   364618672   28808442502 ...
  6 | 1 2752 406396 132202038 28808442502 6544911081900 ...
     ...

Crossrefs

Rows 1..5 are A000012, A339760, A339761, A339762, A339763.

Main diagonal is A308129.

Cf. A272445, A307026, A329118, A339098, A339190.

Sequence in context: A174148 A155495 A157273 * A168518 A174667 A174672

Adjacent sequences: A350726 A350727 A350728 * A350730 A350731 A350732

Keyword

nonn,tabl

Author

Andrew Howroyd, Jan 16 2022

Status

approved