[seqfan] Question regarding A174283

[Rainer Rosenthal]

Hi all,

there is a comment in A17283 = 1, 2, 4, 9, 22, 53, ... saying:
~~~~~~~~~~~~
The terms of this sequence consider only series and parallel
combinations; A174283 considers bridge combinations as well. - Jon E.
Schoenfield, Sep 02 2013
~~~~~~~~~~~~
For bridge combinations there is A174285 = 0, 0, 0, 0, 1, 3, ...
So I expect A174283 to be the sum, but we have A174283 = 1, 2, 4, 9, 23,
57, ...
There is the same "example 2" provided in A174283 and A174285 to explain
a(6).
I am sure that 53 + 3 is not equal to 57 (proof left to the reader).
So I must be missing something. Can someone please help me?

Cheers,
Rainer