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%I #5 Mar 13 2023 13:31:07
%S 4,12,48,80,480,2880,13440,53760,107520,322560,725760
%N Maximum difficulty level (see A361424 for the definition) for tiling an n X 4 rectangle with a set of integer-sided rectangles, rounded down to the nearest integer.
%C For all currently known terms, the maximum difficulty level is an integer.
%e The following table shows all sets of pieces that give the maximum (n,4)-tiling difficulty level up to n = 11.
%e \ Number of pieces of size
%e n \ 1X1 | 1X2 | 1X3 | 1X4 | 1X5 | 1X6 | 1X7 | 1X8 | 1X10| 2X2 | 2X3 | 2X4
%e ----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+----
%e 1 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
%e 2 | 0 | 2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
%e 2 | 0 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
%e 3 | 0 | 1 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
%e 4 | 0 | 1 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
%e 5 | 0 | 1 | 3 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0
%e 6 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0
%e 6 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0
%e 7 | 0 | 3 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 1 | 0
%e 7 | 0 | 0 | 3 | 2 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0
%e 8 | 0 | 3 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 2 | 0 | 0
%e 9 | 0 | 3 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0
%e 9 | 0 | 3 | 0 | 0 | 0 | 2 | 0 | 1 | 0 | 1 | 1 | 0
%e 9 | 0 | 0 | 3 | 1 | 2 | 1 | 1 | 0 | 0 | 0 | 0 | 0
%e 10 | 0 | 2 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1
%e 11 | 1 | 2 | 0 | 0 | 0 | 0 | 1 | 2 | 0 | 1 | 2 | 0
%e 11 | 1 | 1 | 0 | 0 | 1 | 2 | 0 | 0 | 1 | 2 | 1 | 0
%Y Fourth column of A361424.
%Y Cf. A361220.
%K nonn,more
%O 1,1
%A _Pontus von Brömssen_, Mar 11 2023