[seqfan] need help with seqs from Combinatorics of Lattice QCD at Strong Coupling

[Neil Sloane]

Dear Seqfans, This paper,
W. Unger, Combinatorics of Lattice QCD at Strong Coupling, arXiv preprint
arXiv:1411.4493, 2014
has a table on page 4, in which the first row might be A005789 (actually it
matches several sequences), A123691 (a unique match), followed
by three apparently new sequences.

Could someone look into this? Compute more terms,
add references from the entries to the paper,
create new sequences for the last three rows?
And what about the columns?