OFFSET
1,2
COMMENTS
The position and orientation of each rectangle in a tiling is irrelevant. Squares are allowed.
The first column is A000041 since tiling the n X 1 rectangle (ignoring the order of the tiles) is the same thing as partitioning its length n.
EXAMPLE
Triangle begins
1
2 4
3 10 21
5 22 73 191
7 44 190 698 1999
11 91 507 2276 8498 27016
15 172 1176 6647 29688 116593 390304
22 326 2845 18820 100160 454677 1805924 ...
For w=4, h=4, 3 tiles: one 2 X 1, one 3 X 2, one 4 X 2
aaaa
aaaa
bbbc
bbbc
For w=8, h=7, 14 tiles: one 1 X 1, one 2 X 1, one 2 X 2, six 3 X 1, two 4 X 1, one 4 X 3, one 5 X 1, one 6 X 1
aaaagggl
aaaaffkl
aaaaffkl
bbbbbbkn
cccccjjj
ddddhhhm
eeeeiiim
CROSSREFS
KEYWORD
AUTHOR
Lars Blomberg, Nov 22 2021
STATUS
approved