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A087092
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Descending squares: which squares can be packed with at least 2 squares so that every square directly above a square is strictly smaller? It is conjectured that the answer is all except those in this sequence.
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0
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1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 17, 19, 23, 33
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OFFSET
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1,2
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LINKS
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EXAMPLE
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6, 10 and 25 are not in the sequence: To pack a 6 X 6 square, use 2 3 X 3s on the bottom, 3 2 X 2's above that and 6 1 X 1's on the top. For 10 X 10, use 2 5 X 5s on the bottom, a 4 X 4 and 2 3 X 3s above that; put 4 1 X 1's above the 4 X 4 and 3 2 X 2's above the 3 X 3s. For 25 X 25, use a 15 X 15 and a 10 X 10 on the bottom and 2 5 X 5s above the 10 X 10; above that use a 7 X 7, a 6 X 6 and 3 4 X 4s; the rest can be packed with 3 X 3s, 2 X 2's and 1 X 1's.
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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