rotate, -1 <--> 1, reverse

[Wouter Meeussen]

for the permutations of n 1's and n 0's,
rotation, sign reversal and reversal turn out as 

1       1       1       1*1
2       6       2       1*2+1*4
3       20      3       1*2+1*6+1*12
4       70      7       1*2+1*4+2*8+3*16
5       252     13      1*2+3*10+7*20+2*40
6       924     35      1*2+1*4+1*6+4*12+20*24+8*48
7       3432    85      1*2+7*14+35*28+42*56
8       12870   257     1*2+1*4+2*8+11*16+88*32+154*64


and this gives ansd old familiar


%I A006840 M0837
%S A006840 1,2,3,7,13,35,85,257,765,2518
%N A006840 Binary sequences of period 2n with n 1's per period.
%R A006840 JAuMS A33 14 1982. CN 40 89 1983.
%O A006840 1,2
%A A006840 njas
%K A006840 nonn

this leads me to suspect that the counting strategy using adjacency matrices
has produced some "accidental degeneracies" for the neclace case too.
I'll be trying to get examples of permutations with such "accidental
degeneracies"
in the coming days.
pro memori,
this means that permutations that are not linked by the rotation, sign
reversal and reversal strategy can still produce identical "distance
measures" when using a adjacency matrix strategy.
I don't know about you, but that gets me pretty edgy.

Why hasn't anyone pointed out this before? Or did I miss it?

Looking for close matches between sequences might help fish 'm out.

wouter.
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc at vandemoortele.be
eu000949 at pophost.eunet.be