OFFSET
1,10
COMMENTS
All possible tilings are counted, including those identical by symmetry. Note that distinct dimensions means that, for example, a 2 X 3 rectangle can only be used once, regardless of whether it lies horizontally or vertically.
EXAMPLE
a(2), a(3), a(5), a(7), a(11) = 1 as the only possible tiling is that using an n X n square where n is a prime number. It is likely 11 is the last prime indexed term that equals 1 although this is unknown.
a(10) = 4128. And example tiling is:
.
+---+---+---+---+---+---+---+---+---+---+
| | | |
+ + + +
| | | |
+---+---+---+---+---+---+---+---+---+---+
| | |
+ + +
| | |
+ + +
| | |
+---+---+---+ +
| | |
+ + +
| | |
+ +---+---+---+---+---+---+---+
| | |
+ + +
| | |
+ + +
| | |
+---+---+---+---+---+---+---+---+---+---+
.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, Mar 10 2023
STATUS
approved