A361219 Maximum number of ways in which a set of integer-sided rectangular pieces can tile an n X 3 rectangle.

2, 11, 56, 370, 2666, 19126, 134902, 1026667, 8049132, 60996816, 450456500, 3427769018, 27127841200, 211563038980, 1837421211974, 15474223886906

Offset: 1

Author

Pontus von Brömssen, Mar 05 2023

Keywords

• nonn
• more

Comments

Tilings that are rotations or reflections of each other are considered distinct.

Examples

			The following table shows the sets of pieces that give the maximum number of tilings for n <= 16. All these sets are unique.
    \     Number of pieces of size
   n \  1 X 1 | 1 X 2 | 1 X 3 | 1 X 4
  ----+-------+-------+-------+------
   1  |   1   |   1   |   0   |   0
   2  |   2   |   2   |   0   |   0
   3  |   3   |   3   |   0   |   0
   4  |   3   |   3   |   1   |   0
   5  |   4   |   4   |   1   |   0
   6  |   7   |   4   |   1   |   0
   7  |   8   |   5   |   1   |   0
   8  |   8   |   5   |   2   |   0
   9  |   9   |   6   |   2   |   0
  10  |  10   |   7   |   2   |   0
  11  |  11   |   8   |   2   |   0
  12  |  11   |   8   |   3   |   0
  13  |  12   |   9   |   3   |   0
  14  |  13   |   8   |   3   |   1
  15  |  14   |   9   |   3   |   1
  16  |  15   |  10   |   3   |   1
		

Crossrefs

Third column of A361216.

Cf. A360632, A361225.