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

1,1

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).

Links

Table of n, a(n) for n=1..27.

Example

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.

Sequence in context: A225422 A290518 A242882 * A157285 A320068 A345988

Adjacent sequences: A361423 A361424 A361425 * A361427 A361428 A361429

Keyword

nonn,more

Author

Pontus von Brömssen, Mar 11 2023

Status

approved