Extend Sequence A005966 - trivalent planar multigraphs with 2n nodes

[N. J. A. Sloane]

I can provide a bit more information about the reference.

It is from Chap 5 of the book.
The chapter is

A. T. Balaban, Enumeration of Cyclic Graphs, pp. 63-105 of the book mentioned.

It appears that the numbers were obtained by enumerating all 
multigraphs, and then extracting the planar ones. He stopped at 12 nodes.

Maybe Brendan McKay can extend it!

But let me remind everyone of Fred Lunnon's old saying,
that the last term of any published sequence is likely
to be wrong.

Neil Sloane