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Search: id:A114736
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| A114736 |
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Number of planar partitions of n with distinct part sizes in each row and column. |
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1
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OFFSET
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0,4
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COMMENT
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If these partitions are "flattened" into a simple partition, the resulting partitions are those for which any part size present with multiplicity k implies the presence of at least k(k-1)/2 larger parts. E.g., [3,1|1] flattens to [3,1^2], 1 has multiplicity 2, so there must be at least 2*1/2 = 1 part larger than 1 - which is the 3.
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EXAMPLE
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For n = 5, we have the 6 partitions [5], [4,1], [4|1], [3,2], [3|2], and [3,1|1]. The last has part size 1 twice, but they are in different rows and in different columns.
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CROSSREFS
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Cf. A000219, A117433, A000009.
Sequence in context: A085378 A125869 A059618 this_sequence A099417 A139463 A068922
Adjacent sequences: A114733 A114734 A114735 this_sequence A114737 A114738 A114739
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KEYWORD
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more,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 16 2006
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