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%I #6 Mar 11 2023 08:37:53
%S 1,4,11,29,94,263,968,3416,11520,41912,136972,481388,1743784,6275886,
%T 23615432,93819128,368019576,1367900808,5403282616,19831367476,
%U 76031433360,300581321056,1143307393600,4542840116352,17001097572544,65314285778004,246695766031432
%N Maximum number of ways in which a set of integer-sided rectangular pieces can tile an n X 2 rectangle.
%C Tilings that are rotations or reflections of each other are considered distinct.
%e 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.
%e \ Number of pieces of size
%e n \ 1 X 1 | 1 X 2 | 1 X 3 | 1 X 4
%e ----+-------+-------+-------+------
%e 1 | 2 | 0 | 0 | 0
%e 1 | 0 | 1 | 0 | 0
%e 2 | 2 | 1 | 0 | 0
%e 3 | 2 | 2 | 0 | 0
%e 4 | 4 | 2 | 0 | 0
%e 5 | 4 | 3 | 0 | 0
%e 6 | 4 | 4 | 0 | 0
%e 7 | 5 | 3 | 1 | 0
%e 8 | 5 | 4 | 1 | 0
%e 9 | 7 | 4 | 1 | 0
%e 10 | 7 | 5 | 1 | 0
%e 11 | 7 | 6 | 1 | 0
%e 12 | 9 | 6 | 1 | 0
%e 13 | 8 | 6 | 2 | 0
%e 14 | 10 | 6 | 2 | 0
%e 15 | 10 | 7 | 2 | 0
%e 16 | 10 | 6 | 2 | 1
%e 17 | 10 | 7 | 2 | 1
%e 18 | 12 | 7 | 2 | 1
%e 19 | 12 | 8 | 2 | 1
%e 20 | 12 | 9 | 2 | 1
%e 21 | 13 | 8 | 3 | 1
%e 22 | 13 | 9 | 3 | 1
%e 23 | 15 | 9 | 3 | 1
%e 24 | 15 | 10 | 3 | 1
%e 25 | 15 | 11 | 3 | 1
%e 26 | 17 | 11 | 3 | 1
%e 27 | 17 | 12 | 3 | 1
%Y Second column of A361216.
%Y Cf. A360631, A361224.
%K nonn
%O 1,2
%A _Pontus von Brömssen_, Mar 05 2023
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