A375858 Array T(n,m) read by antidiagonals: In an n X m grid draw straight walls between cells, starting at a border, such that the resulting figure is connected and has only one-cell wide paths; T(n,m) is the number of solutions.

1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 26, 56, 26, 1, 1, 57, 212, 212, 57, 1, 1, 120, 701, 1112, 701, 120, 1, 1, 247, 2179, 4793, 4793, 2179, 247, 1, 1, 502, 6600, 19082, 25000, 19082, 6600, 502, 1, 1, 1013, 19808, 74368, 116852, 116852, 74368, 19808, 1013, 1

Offset: 1

Author

Andrew Howroyd, Aug 31 2024

Keywords

• nonn
• tabl

Comments

See A375770 and A375817 for additional explanation and illustration of solutions.

This sequence counts a subset of the spanning trees enumerated in A116469.

Examples

			Array begins:
==================================================
n/m | 1   2    3     4      5       6        7 ...
----+---------------------------------------------
  1 | 1   1    1     1      1       1        1 ...
  2 | 1   4   11    26     57     120      247 ...
  3 | 1  11   56   212    701    2179     6600 ...
  4 | 1  26  212  1112   4793   19082    74368 ...
  5 | 1  57  701  4793  25000  116852   535776 ...
  6 | 1 120 2179 19082 116852  607712  3048668 ...
  7 | 1 247 6600 74368 535776 3048668 15918280 ...
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 antidiagonals)

Crossrefs

Main diagonal is A375817.

Cf. A116469, A375770, A375859, A375860, A375861.

Programs

PARI

\\ A375858(n,m) defined in PARI link in A375770.

Formula

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