|
|
A067281
|
|
Number of permutations of {1,2,3,...,n} where the elements of n are considered indistinguishable if they differ by a power of 2 (for example 3, 12 and 24 are all considered equivalent).
|
|
2
|
|
|
1, 1, 1, 3, 4, 20, 60, 420, 840, 7560, 37800, 415800, 1663200, 21621600, 151351200, 2270268000, 7264857600, 123502579200, 1111523212800, 21118941043200, 140792940288000, 2956651746048000, 32523169206528000, 748032891750144000, 4488197350500864000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
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...}.
|
|
LINKS
|
|
|
EXAMPLE
|
a(6) = 20 since {1,2,3,4,5,6} becomes {1,1,3,1,5,3} which has 60 permutations.
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Brian Rothbach (rothbach(AT)math.berkeley.edu), Feb 23 2002
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|