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A361413
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Number of ways to tile an n X n square using rectangles with distinct dimensions where all the rectangle edge lengths are prime numbers.
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0
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0, 1, 1, 0, 1, 0, 1, 0, 0, 4128, 1, 10880, 641, 45904, 349496, 892088, 40873, 17695080
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OFFSET
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1,10
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COMMENTS
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All possible tilings are counted, including those identical by symmetry. Note that distinct dimensions means that, for example, a 2 X 3 rectangle can only be used once, regardless of whether it lies horizontally or vertically.
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LINKS
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EXAMPLE
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a(2), a(3), a(5), a(7), a(11) = 1 as the only possible tiling is that using an n X n square where n is a prime number. It is likely 11 is the last prime indexed term that equals 1 although this is unknown.
a(10) = 4128. And example tiling is:
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+---+---+---+---+---+---+---+---+---+---+
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+ + + +
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+---+---+---+---+---+---+---+---+---+---+
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+ + +
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+ + +
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+---+---+---+ +
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+ + +
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+ +---+---+---+---+---+---+---+
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+ + +
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+ + +
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+---+---+---+---+---+---+---+---+---+---+
.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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