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A361219 Maximum number of ways in which a set of integer-sided rectangular pieces can tile an n X 3 rectangle. 4

%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 integer-sided 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 Brömssen_, Mar 05 2023

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Last modified April 15 11:16 EDT 2024. Contains 371681 sequences. (Running on oeis4.)