A361218 Maximum number of ways in which a set of integer-sided rectangular pieces can tile an n X 2 rectangle.
1, 4, 11, 29, 94, 263, 968, 3416, 11520, 41912, 136972, 481388, 1743784, 6275886, 23615432, 93819128, 368019576, 1367900808, 5403282616, 19831367476, 76031433360, 300581321056, 1143307393600, 4542840116352, 17001097572544, 65314285778004, 246695766031432
Offset: 1
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The following table shows the sets of pieces that give the maximum number of tilings for n <= 27. The solutions are unique except for n = 1.
\ Number of pieces of size
n \ 1 X 1 | 1 X 2 | 1 X 3 | 1 X 4
----+-------+-------+-------+------
1 | 2 | 0 | 0 | 0
1 | 0 | 1 | 0 | 0
2 | 2 | 1 | 0 | 0
3 | 2 | 2 | 0 | 0
4 | 4 | 2 | 0 | 0
5 | 4 | 3 | 0 | 0
6 | 4 | 4 | 0 | 0
7 | 5 | 3 | 1 | 0
8 | 5 | 4 | 1 | 0
9 | 7 | 4 | 1 | 0
10 | 7 | 5 | 1 | 0
11 | 7 | 6 | 1 | 0
12 | 9 | 6 | 1 | 0
13 | 8 | 6 | 2 | 0
14 | 10 | 6 | 2 | 0
15 | 10 | 7 | 2 | 0
16 | 10 | 6 | 2 | 1
17 | 10 | 7 | 2 | 1
18 | 12 | 7 | 2 | 1
19 | 12 | 8 | 2 | 1
20 | 12 | 9 | 2 | 1
21 | 13 | 8 | 3 | 1
22 | 13 | 9 | 3 | 1
23 | 15 | 9 | 3 | 1
24 | 15 | 10 | 3 | 1
25 | 15 | 11 | 3 | 1
26 | 17 | 11 | 3 | 1
27 | 17 | 12 | 3 | 1
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