[seqfan] Counting cycles in graphs - was Re: A200000

[Olivier Gerard]

On Tue, Nov 15, 2011 at 06:00, Andrew Weimholt <andrew.weimholt at gmail.com>wrote:

>
> T(n,k), with rows containing (in ascending order) the possible values
> of numbers of cycles on a graph with n nodes.
>
>    0,
>    0,
>    0,
>    0, 1
>    0, 1, 3, 7,
>    0, 1, 2, 3, 6, 7, 12, 13, 22, 37,
>    0, 1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21,
> 22, 23, 24, 30, 32, 33, 35, 36, 37, 38, 39, 52, 53, 54, 59, 63, 85,
> 91, 133, 197
>
> The row lengths of the above triangle are…
>
>    1, 1, 1, 2, 4, 10, 38, 160, 830, 5223,
>
>
Dear Andrew,

Very good one. I didn't think it was not in the OEIS.

Have you calculated the weighted version?

By this, I mean for each n, the sum of all the number of cycles of all the
graphs with n nodes?

I would very much like to see both in the OEIS (and the associated
triangles).

Regards,

Olivier