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Search: id:A094198
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| A094198 |
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Number of ways that n boxes with distinct sizes can contain each other under the condition that each box may contain at most three (themselves possibly nested) boxes. Each box is assumed to be large enough to contain any three smaller boxes. |
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+0
1
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| 1, 2, 6, 24, 119, 702, 4795, 37183, 322486, 3091630, 32453172, 370104159, 4555518746, 60182704891, 849245520581, 12746759647944, 202753756944382, 3406596290534764, 60282041591986049, 1120554350714688130
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If each box may contain at most one (possibly nested) box then the Bell numbers (A000110) are obtained, whereas if each box may contain at most two smaller (possibly nested) boxes then A000772 is obtained, and if no restriction is placed on the number of (possible nested) boxes that any box may contain then the factorial numbers (A000142) are obtained. Sequence suggested by an earlier submission of Rick L. Shepherd (rshepherd2(AT)hotmail.com).
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EXAMPLE
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a(3)=6, as seen from these arrangements: 112233, 321123, 311223, 211233, 223113, 113223, where xyyx indicates that box x contains box y, etc.
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CROSSREFS
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Cf. A000110, A000142, A000772.
Adjacent sequences: A094195 A094196 A094197 this_sequence A094199 A094200 A094201
Sequence in context: A095818 A052397 A047889 this_sequence A071077 A005395 A092495
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), May 25 2004
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