# [seqfan] Re: unlabeled Motzkin numbers

Max Alekseyev maxale at gmail.com
Fri Oct 29 04:16:14 CEST 2010

```Manually, I've got that the sequence of unlabeled Motzkin numbers starts with:
1,2,2,4,5,12,19,...
and this sequence is not in the OEIS.

In particular:
for n=1, there is one configuration (the empty one) of period 1
for n=2, there are two configurations both of period 1
for n=3, there are one configuration of period 1 and one of period 3
for n=4, there are one configuration of period 1, two of period 2, and
one of period 4
for n=5, there are one configuration of period 1 and four of period 5
for n=6, there are one configuration of period 1, one of period 2,
four of period 3, and six of period 6
( check: 1*1 + 1*2 + 4*3 + 6*6 = 51 = A001006(6) )

For odd prime p, we have
a(p) = (A001006(p) - 1)/p + 1

Max

On Wed, Oct 27, 2010 at 2:40 PM, Max Alekseyev <maxale at gmail.com> wrote:
> Just out of curiosity, what would be an "unlabeled" version of Motzkin
> numbers A001006?
> That is, number of ways of drawing any number of nonintersecting
> chords joining n unlabeled equally spaced points on a circle (in other
> words, the points and chords are distinguished up to rotations of the
> circle).
> Is this sequence in the OEIS?
>
> Furthermore, is there a variant of counting up to rotations and
> reflections of the circle?
>
> Regards,
> Max
>

```