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Number of ways to tile an n X n square using oblongs with distinct height x width dimensions.
3

%I #4 Feb 18 2023 08:08:43

%S 0,0,4,36,1056,31052,1473944,87469884

%N Number of ways to tile an n X n square using oblongs with distinct height x width dimensions.

%C All possible tilings are counted, including those identical by symmetry. Note that distinct height x width dimensions means that, for example, a 1 x 3 oblong can be used twice, once in a horizonal (1 x 3) and once in a vertical (3 x 1) direction.

%e a(1) = 0 as no distinct oblongs can tile a square with dimensions 1 x 1.

%e a(2) = 0 as no distinct oblongs can tile a square with dimensions 2 x 2.

%e a(3) = 4. There is one tiling, excluding those equivalent by symmetry:

%e .

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%e This tiling can occur in 4 different ways, giving 4 ways in total.

%e a(4) = 36. The possible tilings, excluding those equivalent by symmetry, are:

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%e .

%e The first tiling can occur in 8 different ways, the second in 4 different ways, the third in 16 different ways and the fourth in 8 different ways. This gives 36 ways in total.

%Y Cf. A360256 (rectangles), A360499, A360498, A182275, A004003, A099390, A065072.

%K nonn,more

%O 1,3

%A _Scott R. Shannon_, Feb 18 2023