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.
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
Examples
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 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 antidiagonals)
Formula
T(n,m) = T(m,n).
Comments