%I #5 Mar 11 2023 08:37:58
%S 2,11,56,370,2666,19126,134902,1026667,8049132,60996816,450456500,
%T 3427769018,27127841200,211563038980,1837421211974,15474223886906
%N Maximum number of ways in which a set of integersided rectangular pieces can tile an n X 3 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 <= 16. All these sets are unique.
%e \ Number of pieces of size
%e n \ 1 X 1  1 X 2  1 X 3  1 X 4
%e ++++
%e 1  1  1  0  0
%e 2  2  2  0  0
%e 3  3  3  0  0
%e 4  3  3  1  0
%e 5  4  4  1  0
%e 6  7  4  1  0
%e 7  8  5  1  0
%e 8  8  5  2  0
%e 9  9  6  2  0
%e 10  10  7  2  0
%e 11  11  8  2  0
%e 12  11  8  3  0
%e 13  12  9  3  0
%e 14  13  8  3  1
%e 15  14  9  3  1
%e 16  15  10  3  1
%Y Third column of A361216.
%Y Cf. A360632, A361225.
%K nonn,more
%O 1,1
%A _Pontus von BrÃ¶mssen_, Mar 05 2023
