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Search: id:A054243
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| A054243 |
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Number of partitions of n into distinct positive parts <=n, where parts are combined by XOR. |
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+0
5
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| 1, 1, 1, 2, 2, 4, 8, 16, 16, 32, 64, 128, 256, 512, 1024, 2048, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 67108864, 134217728, 268435456, 536870912
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Usually successive powers of 2, but "stutters" when n is power of 2. (G.f. must satisfy some interesting functional equations!). Empty partition of 0 defined as 1.
This is an instance of what I like to call "numbral theory": whenever you have a set of indexed objects that you can do some kind of arithmetic on, then the indices act as "shadows" of the objects and you can generally talk about lots of analogs, such as partitions, primes, even generating functions, etc. It would be worthwhile to systematically "fill out" the entries for as many of these systems as possible in the OEIS.
The "AND" version is just the all-ones sequence. - Christian G. Bower (bowerc(AT)usa.net), Jun 07 2005
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FORMULA
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a(n) = 2^[n-log2(n)-1] = A000079(n)/A062383(n). - Henry Bottomley (se16(AT)btinternet.com), Nov 22 2001
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EXAMPLE
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a(5)=4 thus: 5 4+1 5+3+2+1 4+3+2 (where "+" = XOR)
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CROSSREFS
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Inclusive-OR (or IOR) version: A054244.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)
Cf. A160473.
(End)
Sequence in context: A153999 A154002 A154005 this_sequence A005864 A112433 A090129
Adjacent sequences: A054240 A054241 A054242 this_sequence A054244 A054245 A054246
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Feb 08 2000
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