login
A349575
Triangle read by rows: T(w,h) (for w >= h >= 1) is the number of distinct sets of rectangles with integer sides that tile the w X h rectangle.
0
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
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
Sequence in context: A014664 A270600 A350231 * A360629 A180871 A305423
KEYWORD
nonn,tabl,more
AUTHOR
Lars Blomberg, Nov 22 2021
STATUS
approved