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A114736
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Number of planar partitions of n where parts strictly decrease along each row and column.
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0
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1, 1, 1, 3, 4, 6, 10, 15, 22, 33, 49, 70, 102, 146, 205, 290, 405, 561, 779, 1071, 1463, 1999, 2714, 3667, 4946, 6641, 8880, 11848, 15753, 20870, 27586, 36354, 47766, 62621, 81878, 106785, 138975, 180449, 233778, 302270
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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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REFERENCES
| B. Gordon, Multirowed partitions with strict decrease along columns (Notes on plane partitions IV.), Symposia Amer. Math. Soc. 19 (1971) 91-100.
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EXAMPLE
| For n = 5, we have the 6 partitions [5], [4,1], [4|1], [3,2], [3|2] and [3,1|1].
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CROSSREFS
| Cf. A000219, A117433, A000009.
Sequence in context: A171096 A125869 A059618 * A099417 A139463 A068922
Adjacent sequences: A114733 A114734 A114735 * A114737 A114738 A114739
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KEYWORD
| more,nonn
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 16 2006
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EXTENSIONS
| Clarified definition, added 30 terms and reference. - Dennis K Moore, Jan 12 2011
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