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

1,3

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.

Links

Table of n, a(n) for n=1..9.

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

Adjacent sequences: A360495 A360496 A360497 * A360499 A360500 A360501

Keyword

nonn,more

Author

Scott R. Shannon, Feb 09 2023

Status

approved