A361427 Maximum difficulty level (see A361424 for the definition) for tiling an n X 3 rectangle with a set of integer-sided rectangles, rounded down to the nearest integer.

2, 6, 8, 48, 80, 480, 960, 1920, 3360, 13440, 20160, 60480, 80640, 201600, 967680, 1612800

Offset: 1

Author

Pontus von Brömssen, Mar 11 2023

Keywords

• nonn
• more

Comments

For all currently known terms, the maximum difficulty level is an integer.

Examples

			The following table shows all sets of pieces that give the maximum (n,3)-tiling difficulty level up to n = 16.
    \               Number of pieces of size
   n \ 1X1|1X2|1X3|1X4|1X5|1X6|1X7|1X8|1X9|1X10|1X12|2X2|2X3|2X4|2X5
  ----+---+---+---+---+---+---+---+---+---+----+----+---+---+---+---
   1  | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   1  | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   2  | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   3  | 1 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   4  | 0 | 1 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   5  | 0 | 3 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   5  | 0 | 1 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 0 | 0
   6  | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 0 | 0
   7  | 0 | 3 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 0 | 0
   7  | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0  | 0  | 0 | 1 | 0 | 0
   8  | 0 | 3 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0  | 0  | 0 | 1 | 0 | 0
   9  | 4 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0  | 0  | 1 | 1 | 0 | 0
   9  | 2 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0  | 0  | 1 | 1 | 0 | 0
   9  | 0 | 4 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0  | 0  | 1 | 0 | 0 | 0
   9  | 0 | 3 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0  | 0  | 2 | 0 | 0 | 0
  10  | 3 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 0 | 1
  11  | 0 | 2 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 1  | 0  | 0 | 1 | 0 | 0
  12  | 3 | 0 | 0 | 2 | 0 | 0 | 1 | 0 | 0 | 0  | 0  | 2 | 0 | 0 | 1
  13  | 1 | 0 | 1 | 2 | 1 | 0 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 1 | 1
  13  | 0 | 2 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0  | 1  | 1 | 1 | 0 | 0
  14  | 4 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0  | 0  | 1 | 0 | 2 | 0
  14  | 3 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 1 | 0  | 0  | 3 | 0 | 0 | 1
  14  | 2 | 0 | 0 | 2 | 4 | 0 | 0 | 0 | 0 | 0  | 0  | 1 | 0 | 1 | 0
  15  | 1 | 0 | 0 | 3 | 2 | 1 | 0 | 0 | 0 | 0  | 0  | 0 | 1 | 0 | 1
  16  | 3 | 0 | 0 | 2 | 1 | 1 | 0 | 0 | 0 | 0  | 0  | 0 | 0 | 2 | 1
		

Crossrefs

Third column of A361424.

Cf. A360632, A361219, A361225.