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A375861
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 up to symmetries of the rectangle.
3
1, 1, 1, 1, 2, 1, 1, 5, 5, 1, 1, 9, 19, 9, 1, 1, 19, 63, 63, 19, 1, 1, 35, 192, 298, 192, 35, 1, 1, 71, 576, 1246, 1246, 576, 71, 1, 1, 135, 1698, 4857, 6351, 4857, 1698, 135, 1, 1, 271, 5042, 18768, 29467, 29467, 18768, 5042, 271, 1, 1, 527, 14963, 72968, 134397, 152516, 134397, 72968, 14963, 527, 1
OFFSET
1,5
COMMENTS
See A375770 and A375860 for additional explanation and illustration of solutions.
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 2 5 9 19 35 71 ...
3 | 1 5 19 63 192 576 1698 ...
4 | 1 9 63 298 1246 4857 18768 ...
5 | 1 19 192 1246 6351 29467 134397 ...
6 | 1 35 576 4857 29467 152516 763479 ...
7 | 1 71 1698 18768 134397 763479 3982186 ...
...
PROG
(PARI) \\ A375861(n, m) defined in PARI link in A375770.
CROSSREFS
Main diagonal is A375860.
Cf. A375858 (not reduced for symmetry).
Sequence in context: A197342 A197217 A197242 * A128564 A196636 A196641
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Aug 31 2024
STATUS
approved