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Search: id:A067601
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| A067601 |
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a(n) is the number of inequivalent permutations of {0..2n-1}, such that the first differences (modulo 2n) are a permutation of {1..2n-1}. |
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+0
1
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OFFSET
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1,3
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COMMENT
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"Inequivalent" effectively means that the permutation begins with 0 and the second item is <= N. (Working modulo 2n, s1+k,s2+k,s3+k... is equivalent to s1,s2,s3,...; and -s1,-s2,-s3 is equivalent to s1,s2,s3,...)
The references all deal with length 12.
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REFERENCES
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Stefan Bauer-Mengelberg and Melvin Ferentz, On Eleven-Interval Twelve-Tone Rows, Perspectives of New Music 3, no. 2 (Spring-Summer 1965): 93-103
Robert Morris and Daniel Starr, The Structure of All-interval Series, Journal of Music Theory 18, no. 2 (Fall 1974): 364-389
David Schiff, Elliott Carter's Harvest Home, Tempo 167 (December 1988): 7-13
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EXAMPLE
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0 1 3 2 has first difference, mod 4, of 1 2 3; 0 2 1 4 5 3 has first difference, mod 6, of 2 5 3 1 4; 0 4 5 8 3 1 7 9 2 11 10 6 has first difference, mod 12, of 4 1 3 7 10 6 2 5 9 11 8
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CROSSREFS
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Sequence in context: A091144 A087800 A009747 this_sequence A052740 A052742 A035049
Adjacent sequences: A067598 A067599 A067600 this_sequence A067602 A067603 A067604
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KEYWORD
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nonn
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AUTHOR
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Eugene McDonnell (eemcd(AT)aol.com), Jan 31 2002
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Oct 31 2005
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