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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.
1
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).
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.
Sequence in context: A225422 A290518 A242882 * A157285 A320068 A345988
KEYWORD
nonn,more
AUTHOR
STATUS
approved