More on Interval Vectors

The sequence 1,1,2,3,7,13,35,85,254,701,2377,7944,25220...
appears on the Encyclopedia of Integer Sequences(A045611) as the
"Number of different energy states of n positive and n negative
charges on a necklace.." This sequence also corresponds to Intvec
(2n,n)for n=(0...12). This caused me to search the EIS for other
interesting sequences.

A045612 is kind of interesting. It is the "Number of different energy
states between two stacked necklaces, each of n positive and n
negative charges." I got to thinking that it might be fun to take
(for example) all the different pairs of hexachords (in 12-et) and
compute this for them. This can then be used to represent all the
voice-leading potentialities between hexachords. The vector used
for A045612 is different in that it now must include 0 as well
as 1,2,3,4,5,6. Once again, you get Z-relations, which I would like
to call Z2-relations because you are comparing 2 necklaces
(hexachords). I will call the main function Intvec2(2n,n)

Just to prove A045612, here are the 5 interval vectors for Intvec2
(4,2): (0,4,0), (2,0,2) (2,2,0), (0,2,2) and (1,2,1), which appears
twice. This makes 5 interval vectors (or energy states). The counts
are for (0,1,2) distances. I'll do my computations for hexachords
and post them soon.

Paul Hj