A067601 - OEIS

%I #27 Dec 22 2023 23:59:55

%S 1,1,2,12,144,1928,44664,1377984,51826560

%N 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}.

%C "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,...)

%C The references all deal with length 12.

%H Stefan Bauer-Mengelberg and Melvin Ferentz, <a href="http://www.jstor.org/stable/832507">On Eleven-Interval Twelve-Tone Rows</a>, Perspectives of New Music 3, no. 2 (Spring-Summer 1965): 93-103

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a067/A067601.java">Java program</a> (github)

%H Robert Morris and Daniel Starr, <a href="http://www.jstor.org/stable/843642">The Structure of All-interval Series</a>, Journal of Music Theory 18, no. 2 (Fall 1974): 364-389.

%H David Schiff, <a href="http://www.jstor.org/stable/945209">Elliott Carter's Harvest Home</a>, Tempo 167 (December 1988): 7-13.

%F a(n) = ceiling(A141599(n)/2). - _Leo C. Stein_, Nov 26 2016

%e 0 1 3 2 has first difference, mod 4, of 1 2 3;

%e 0 2 1 4 5 3 has first difference, mod 6, of 2 5 3 1 4;

%e 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.

%Y Cf. A141598, A141599.

%K nonn,more

%O 1,3

%A Eugene McDonnell (eemcd(AT)aol.com), Jan 31 2002

%E Edited by _Don Reble_, Oct 31 2005

%E a(9) from _Sean A. Irvine_, Dec 22 2023