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Search: id:A087092
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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
1
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| 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 17, 19, 23, 33
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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E. Friedman, Illustrations
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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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Sequence in context: A115405 A056867 A062491 this_sequence A046684 A082377 A133811
Adjacent sequences: A087089 A087090 A087091 this_sequence A087093 A087094 A087095
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KEYWORD
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nonn,fini,full
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AUTHOR
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Erich Friedman (erich.friedman(AT)stetson.edu), Oct 19 2003
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Oct 24 2003
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