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

1,1

Comments

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

Links

Table of n, a(n) for n=1..16.

Example

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.

Sequence in context: A198769 A037554 A106804 * A213098 A041129 A332524

Adjacent sequences: A361216 A361217 A361218 * A361220 A361221 A361222

Keyword

nonn,more

Author

Pontus von Brömssen, Mar 05 2023

Status

approved