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%I #5 Mar 11 2023 08:38:24
%S 1,5,8,95,682,4801,33807
%N Maximum number of ways in which a set of integer-sided rectangular pieces can tile an n X 3 rectangle, up to rotations and reflections.
%e The following table shows the sets of pieces that give the maximum number of tilings for n <= 7. The solutions are unique except for n = 1 and n = 3.
%e \ Number of pieces of size
%e n \ 1 X 1 | 1 X 2 | 1 X 3
%e ---+-------+-------+------
%e 1 | 3 | 0 | 0
%e 1 | 1 | 1 | 0
%e 1 | 0 | 0 | 1
%e 2 | 2 | 2 | 0
%e 3 | 3 | 3 | 0
%e 3 | 2 | 2 | 1
%e 4 | 3 | 3 | 1
%e 5 | 4 | 4 | 1
%e 6 | 7 | 4 | 1
%e 7 | 8 | 5 | 1
%e It seems that all optimal solutions for A361219 are also optimal here, but for n = 1 and n = 3 there are other optimal solutions.
%Y Third column of A361221.
%Y Cf. A361219, A360632.
%K nonn,more
%O 1,2
%A _Pontus von Brömssen_, Mar 05 2023