A378938 Array read by antidiagonals: T(m,n) is the number of Hamiltonian paths in an m X n grid which start in the top left corner.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 8, 4, 1, 1, 5, 17, 17, 5, 1, 1, 6, 38, 52, 38, 6, 1, 1, 7, 78, 160, 160, 78, 7, 1, 1, 8, 164, 469, 824, 469, 164, 8, 1, 1, 9, 332, 1337, 3501, 3501, 1337, 332, 9, 1, 1, 10, 680, 3750, 16262, 22144, 16262, 3750, 680, 10, 1

Offset: 1

Author

Andrew Howroyd, Dec 20 2024

Keywords

• nonn
• tabl

Comments

These paths are also called Greek-key tours. The path can end anywhere.

Examples

			Array begins:
======================================================
m\n | 1 2   3    4     5      6        7         8 ...
----+-------------------------------------------------
  1 | 1 1   1    1     1      1        1         1 ...
  2 | 1 2   3    4     5      6        7         8 ...
  3 | 1 3   8   17    38     78      164       332 ...
  4 | 1 4  17   52   160    469     1337      3750 ...
  5 | 1 5  38  160   824   3501    16262     68591 ...
  6 | 1 6  78  469  3501  22144   144476    899432 ...
  7 | 1 7 164 1337 16262 144476  1510446  13506023 ...
  8 | 1 8 332 3750 68591 899432 13506023 180160012 ...
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..435 (first 29 antidiagonals)

Crossrefs

Main diagonal is A145157.

Rows 1..8 are A000012, A000027, A046994, A046995, A145156, A160240, A160241, A374307.

Cf. A332307, A064298, A271465, A271592, A288518.

Formula

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