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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.

Table of values

n a(n)
1 1
2 1
3 1
4 1
5 4
6 1
7 1
8 11
9 11
10 1
11 1
12 26
13 56
14 26
15 1
16 1
17 57
18 212
19 212
20 57
21 1
22 1
23 120
24 701
25 1112
26 701
27 120
28 1
29 1
30 247
31 2179
32 4793
33 4793
34 2179
35 247
36 1
37 1
38 502
39 6600
40 19082
41 25000
42 19082
43 6600
44 502
45 1
46 1
47 1013
48 19808
49 74368
50 116852
51 116852
52 74368
53 19808
54 1013
55 1

List of values

[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]