[seqfan] Re: [A003094: Connected planar graphs with n nodes]

[Christian G.Bower]

"Eric W. Weisstein" <eww at wolfram.com> wrote:
> ID Number: A003094 (Formerly M1652)
> Sequence:  1,1,1,2,6,20,99,646,5974,71885,1052805,17449299
>                         ^^
> Name:      Connected planar graphs with n nodes.
...
> I get a(6)=100 instead of a(6)=99 when I compute the above sequence.
>
> Since my counts agree for planar and connected graphs separately
>
> A005470 1,2,4,11,33,142  Planar graphs with n nodes
> A001349 1,1,2,6,21,112   Connected graphs with n nodes
...
> In any case, can someone double-check the count of planar
> connected graphs on 6 nodes?

Well, I'm not counting planar graphs, but I do know that A003094 is the
inverse Euler transform of A005470. If your counts for A005470 are
correct, then A003094(6)=99.

Consider that
142=
99<6>+
20<5+1>+
6<4+2>+
6<4+1+1>+
3<3+3>+
2<3+2+1>+
2<3+1+1+1>+
1<2+2+2>+
1<2+2+1+1>+
1<2+1+1+1+1>+
1<1*6>

Christian


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