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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.
3
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.
Sequence in context: A154983 A324916 A156534 * A168287 A221987 A285357
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Aug 31 2024
STATUS
approved