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Search: id:A067281
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| A067281 |
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Number of permutations of {1,2,3,...,n} where the elements of n are considered indistinguishable if they they differ by a power of 2 (for example 3, 12 and 24 are all considered equivalent). |
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1
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| 1, 1, 3, 4, 20, 60, 420, 840, 7560, 37800, 415800, 1663200, 21621600, 151351200, 2270268000, 7264857600, 123502579200, 1111523212800, 21118941043200, 140792940288000, 2956651746048000, 32523169206528000, 748032891750144000
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OFFSET
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1,3
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COMMENT
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Alternatively, one can think of these sequences as permutation of {1,2,...,n} where the term n corresponds to the appropriate ideal in Z[1/2]. This description gives an obvious generalization to Z[1/n] or other localizations of Z.
The conjecture a(2n+1)=(2n+1)a(2n) is obviously true from the definition of the sequence and the fact that 2n+1 is the smallest element of its equivalence class. - Brian Rothbach (rothbach(AT)Math.Berkeley.EDU), Sep 15 2004
a(2n+1) = (2n+1)*a(2n). However, a(n+1)/a(n) is non-integral for n = {3, 15, 19...}.
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EXAMPLE
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a(6)=20 since {1,2,3,4,5,6} becomes {1,1,3,1,5,3} which has 60 permutations.
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CROSSREFS
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Cf. A000265.
Sequence in context: A124631 A062870 A151419 this_sequence A151357 A009169 A069934
Adjacent sequences: A067278 A067279 A067280 this_sequence A067282 A067283 A067284
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KEYWORD
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easy,nonn
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AUTHOR
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Brian Rothbach (rothbach(AT)math.berkeley.edu), Feb 23 2002
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 09 2002
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