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

Author

Andrew Howroyd, Jan 16 2022

Keywords

• nonn
• tabl

Examples

			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 ...
     ...
		

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

Crossrefs

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

Main diagonal is A308129.

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

Formula

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