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A334905
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a(n) is the minimum remaining space when a square n X n is tiled with smaller squares with distinct integer sides parallel to the n X n square.
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1
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1, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 21, 30, 29, 20, 25, 30, 12, 19, 24, 17, 13, 13, 18, 14, 19, 14, 15, 15, 15, 20, 15, 20, 16, 22, 16, 16, 17, 21, 22, 15, 13, 16, 18, 14, 14, 14, 17, 15, 11, 10, 12, 13, 4, 11, 8, 9, 7, 11, 4, 9, 8, 8, 8, 6, 8
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OFFSET
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1,2
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COMMENTS
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See (Gambini, 1999) for a way to construct the sequence. Actually, one would have to extend Gambini's idea by putting extra 1-sided squares in the list of "usable squares" to allow finding nonzero-waste packings.
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LINKS
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EXAMPLE
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For n=5, squares of sides {1, 4} can be packed inside the container, leading to uncovered area a(5) = 5*5 - (4*4 + 1*1) = 8. The other maximal packable set is composed of the squares sided {1,2,3}, which would lead to uncovered area greater than 8.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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