A361225 Maximum number of ways in which a set of integer-sided rectangular pieces can tile an n X 3 rectangle, up to rotations and reflections.

1, 5, 8, 95, 682, 4801, 33807

Offset: 1

Author

Pontus von Brömssen, Mar 05 2023

Keywords

• nonn
• more

Examples

			The following table shows the sets of pieces that give the maximum number of tilings for n <= 7. The solutions are unique except for n = 1 and n = 3.
   \ Number of pieces of size
  n \  1 X 1 | 1 X 2 | 1 X 3
  ---+-------+-------+------
  1  |   3   |   0   |   0
  1  |   1   |   1   |   0
  1  |   0   |   0   |   1
  2  |   2   |   2   |   0
  3  |   3   |   3   |   0
  3  |   2   |   2   |   1
  4  |   3   |   3   |   1
  5  |   4   |   4   |   1
  6  |   7   |   4   |   1
  7  |   8   |   5   |   1
It seems that all optimal solutions for A361219 are also optimal here, but for n = 1 and n = 3 there are other optimal solutions.
		

Crossrefs

Third column of A361221.

Cf. A361219, A360632.