# [seqfan] Re: unlabeled Motzkin numbers

Max Alekseyev maxale at gmail.com
Fri Oct 29 05:57:40 CEST 2010

```More terms:

1, 2, 2, 4, 5, 12, 19, 46, 95, 230, 528

I'd be grateful if somebody double check these values.

Regards,
Max

On Thu, Oct 28, 2010 at 10:16 PM, Max Alekseyev <maxale at gmail.com> wrote:
> 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
>>
>

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