Duplicates - which one is wrong?

[Brendan McKay]

* Gordon Royle <gordon at csse.uwa.edu.au> [050801 18:39]:
> The two sequences
> http://www.research.att.com/projects/OEIS?Anum=A000421
> http://www.research.att.com/projects/OEIS?Anum=A005965
> are both meant to be connected cubic multigraphs...
> 
> Firstly, they are duplicates, and secondly, one of them is different  
> to the other - in particular there are apparently 506, or maybe 509,  
> connected cubic multigraphs on 12 vertices.

I also get 509.  I suspect A005965 is merely incorrect, but someone
should check the source.

Therefore, if someone happens to have A. T. Balaban, Enumeration
of Cyclic Graphs, pp. 63-105 of A. T. Balaban, ed., Chemical
Applications of Graph Theory, Ac. Press, 1976; please check page 92
and tell us the exact definition of the sequence 1,2,6,20,91,506.
The "cyclic" in Balaban's title suggests there is some condition.

Brendan.