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A360498
Number of ways to tile an n X n square using oblongs with distinct dimensions.
5
0, 0, 4, 12, 256, 3620, 87216, 2444084, 87181220
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 oblong can only be used once, regardless of if it lies horizontally or vertically.
EXAMPLE
a(1) = 0 as no distinct oblongs can tile a square with dimensions 1 x 1.
a(2) = 0 as no distinct oblongs can tile a square with dimensions 2 x 2.
a(3) = 4. There is one tiling, excluding those equivalent by symmetry:
.
+---+---+---+
| |
+---+---+---+
| |
+ +
| |
+---+---+---+
.
This tiling can occur in 4 different ways, giving 4 ways in total.
a(4) = 12. The possible tilings, excluding those equivalent by symmetry, are:
.
+---+---+---+---+ +---+---+---+---+
| | | | |
+ + + +---+---+---+---+
| | | | |
+---+---+---+---+ + +
| | | |
+ + + +
| | | |
+---+---+---+---+ +---+---+---+---+
.
The first tiling can occur in 8 different way and the second in 4 different ways, giving 12 ways in total.
CROSSREFS
Cf. A360499 (rectangles), A004003, A099390, A065072, A233320, A230031.
Sequence in context: A131491 A286881 A366822 * A291098 A009506 A299808
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, Feb 09 2023
STATUS
approved