A361428 Maximum difficulty level (see A361424 for the definition) for tiling an n X 4 rectangle with a set of integer-sided rectangles, rounded down to the nearest integer.

4, 12, 48, 80, 480, 2880, 13440, 53760, 107520, 322560, 725760

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..11.

Example

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

Crossrefs

Fourth column of A361424.

Cf. A361220.

Sequence in context: A035310 A022016 A151441 * A032380 A057346 A255230

Adjacent sequences: A361425 A361426 A361427 * A361429 A361430 A361431

Keyword

nonn,more

Author

Pontus von Brömssen, Mar 11 2023

Status

approved