A361426 Maximum difficulty level (see A361424 for the definition) for tiling an n X 2 rectangle with a set of integer-sided rectangles, rounded down to the nearest integer.

2, 2, 6, 12, 16, 48, 53, 120, 320, 280, 1120, 2240, 2986, 8960, 17920, 26880, 53760, 107520, 134400, 268800, 537600, 591360, 1182720, 2365440, 2956800, 5677056, 11354112

Offset: 1

Author

Pontus von Brömssen, Mar 11 2023

Keywords

• nonn
• more

Comments

The only cases, currently known to the author, for which the maximum difficulty level is not an integer, are n = 7 (difficulty level 160/3) and n = 13 (difficulty level 8960/3).

Examples

			The following table shows all sets of pieces that give the maximum (n,2)-tiling difficulty level up to n = 27.
    \           Number of pieces of size
   n \  1X1 | 1X2 | 1X3 | 1X4 | 1X5 | 1X7 | 2X2 | 2X3
  ----+-----+-----+-----+-----+-----+-----+-----+----
   1  |  0  |  1  |  0  |  0  |  0  |  0  |  0  |  0
   2  |  0  |  2  |  0  |  0  |  0  |  0  |  0  |  0
   3  |  1  |  1  |  1  |  0  |  0  |  0  |  0  |  0
   4  |  0  |  2  |  0  |  1  |  0  |  0  |  0  |  0
   4  |  0  |  1  |  2  |  0  |  0  |  0  |  0  |  0
   5  |  1  |  2  |  0  |  0  |  1  |  0  |  0  |  0
   5  |  0  |  3  |  0  |  1  |  0  |  0  |  0  |  0
   6  |  0  |  1  |  2  |  1  |  0  |  0  |  0  |  0
   7  |  0  |  1  |  4  |  0  |  0  |  0  |  0  |  0
   8  |  2  |  0  |  2  |  1  |  0  |  0  |  1  |  0
   8  |  0  |  1  |  2  |  1  |  0  |  0  |  1  |  0
   9  |  1  |  0  |  3  |  2  |  0  |  0  |  0  |  0
  10  |  2  |  0  |  2  |  1  |  0  |  0  |  2  |  0
  11  |  1  |  0  |  3  |  2  |  0  |  0  |  1  |  0
  12  |  1  |  0  |  3  |  2  |  0  |  0  |  0  |  1
  12  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  0
  13  |  1  |  0  |  3  |  2  |  0  |  0  |  2  |  0
  14  |  0  |  0  |  4  |  3  |  0  |  0  |  1  |  0
  15  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  1
  16  |  0  |  0  |  4  |  3  |  0  |  0  |  2  |  0
  17  |  0  |  0  |  4  |  3  |  0  |  0  |  1  |  1
  18  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  2
  19  |  0  |  0  |  4  |  3  |  0  |  0  |  2  |  1
  20  |  0  |  0  |  4  |  3  |  0  |  0  |  1  |  2
  21  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  3
  22  |  0  |  0  |  5  |  2  |  0  |  1  |  2  |  1
  22  |  0  |  0  |  5  |  0  |  3  |  0  |  2  |  1
  22  |  0  |  0  |  4  |  3  |  0  |  0  |  2  |  2
  23  |  0  |  0  |  5  |  2  |  0  |  1  |  1  |  2
  23  |  0  |  0  |  5  |  0  |  3  |  0  |  1  |  2
  23  |  0  |  0  |  4  |  3  |  0  |  0  |  1  |  3
  24  |  0  |  0  |  5  |  2  |  0  |  1  |  0  |  3
  24  |  0  |  0  |  5  |  0  |  3  |  0  |  0  |  3
  24  |  0  |  0  |  4  |  3  |  0  |  0  |  0  |  4
  25  |  0  |  0  |  3  |  4  |  0  |  1  |  0  |  3
  26  |  0  |  0  |  5  |  2  |  0  |  1  |  1  |  3
  26  |  0  |  0  |  5  |  0  |  3  |  0  |  1  |  3
  27  |  0  |  0  |  5  |  2  |  0  |  1  |  0  |  4
  27  |  0  |  0  |  5  |  0  |  3  |  0  |  0  |  4
		

Crossrefs

Second column of A361424.

Cf. A360631, A361218, A361224.