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Search: id:A067735
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| A067735 |
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Number of partitions of 2^n into distinct parts. |
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+0
4
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| 1, 1, 2, 6, 32, 390, 16444, 4013544, 11784471548, 1168225267521350, 16816734263788624008200, 276565526698898057002583240473088, 96052644365764024805972019009272150642974291708, 43586702014259316987395017345466711329303914541873541942193666197800
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Always even for n>1 since the only powers of two which are generalized pentagonal numbers (A001318 - needed to produce odd numbers of partitions into distinct terms) are 2^0 and 2^1. Number of digits of A068413 divided by number of digits of a(n) approaches sqrt(2).
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LINKS
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Henry Bottomley, Partition calculators using java applets
Index entries for sequences related to partitions
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FORMULA
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a(n) =A000009(A000079(n))
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EXAMPLE
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a(3)=6 since 2^3=8 can be partitioned into 8, 7+1, 6+2, 5+3, 5+2+1, or 4+3+1.
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MATHEMATICA
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Table[ PartitionsQ[2^n], {n, 0, 13}]
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CROSSREFS
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Cf. A000009, A000079, A068413.
Adjacent sequences: A067732 A067733 A067734 this_sequence A067736 A067737 A067738
Sequence in context: A056642 A001199 A034997 this_sequence A118077 A013976 A083666
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 11 2002
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