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Search: id:A117433
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| A117433 |
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Number of planar partitions of n with all part sizes distinct. |
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+0
2
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| 1, 1, 1, 3, 3, 5, 9, 11, 15, 21, 35, 41, 59, 75, 103, 149, 187, 243, 321, 413, 527, 735, 895, 1165, 1467, 1885, 2335, 2997, 3853, 4765, 5977, 7473, 9269, 11531, 14255, 17537, 22201, 26897, 33233, 40613, 50027, 60637, 74459, 89963, 109751, 134407, 162117
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OFFSET
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0,4
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COMMENT
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Matches A072706 for n < 10, since a unimodal composition into distinct parts can be placed uniquely as a hook. Starting with n = 10, additional partitions are possible (starting with [4,3|2,1] and [4,2|3,1]).
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LINKS
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 01 2008, Table of n, a(n) for n = 0..100
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FORMULA
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a(n) = sum_{k=1}^{floor((sqrt(8*n+1)-1)/2)} A000085(k)*A008289(n,k).
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CROSSREFS
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Cf. A000219, A072706, A117434, A000009.
Sequence in context: A091916 A102437 A072706 this_sequence A078028 A104220 A137202
Adjacent sequences: A117430 A117431 A117432 this_sequence A117434 A117435 A117436
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KEYWORD
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nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 16 2006, Apr 01 2008
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