A360498 Number of ways to tile an n X n square using oblongs with distinct dimensions.

0, 0, 4, 12, 256, 3620, 87216, 2444084, 87181220

Offset: 1

Author

Scott R. Shannon, Feb 09 2023

Keywords

• nonn
• more

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.

Examples

			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.