OFFSET
1,3
COMMENTS
All possible tilings are counted, including those identical by symmetry. Note that distinct dimensions means that, for example, a 1 x 3 rectangle can only be used once, regardless of if it lies horizontally or vertically.
EXAMPLE
a(1) = 1 as the only way to tile a 1 x 1 square is with a square with dimensions 1 x 1.
a(2) = 1 as the only way to tile a 2 x 2 square is with a square with dimensions 2 x 2.
a(3) = 21. The possible tilings, excluding those equivalent by symmetry, are:
.
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
| | | | | | | | | |
+ + +---+---+---+ +---+---+ + +---+---+---+
| | | | | | | | |
+ + + + + + + + +
| | | | | | | | |
+---+---+---+ +---+---+---+ +---+---+---+ +---+---+---+
.
The first tiling can occur in 1 way, the second in 8 different ways, the third in 8 different ways and the fourth in 4 different ways, giving 21 ways in total.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, Feb 09 2023
STATUS
approved