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

1,5

Comments

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

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

Links

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

Formula

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

Example

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 ...
  ...

Prog

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

Crossrefs

Main diagonal is A375817.

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

Sequence in context: A154983 A324916 A156534 * A168287 A221987 A285357

Adjacent sequences: A375855 A375856 A375857 * A375859 A375860 A375861

Keyword

nonn,tabl

Author

Andrew Howroyd, Aug 31 2024

Status

approved