A100092 et al

[David Wilson]

This is in regard to A100092, the number of n-ominoes of minimal
perimeter 2*ceil(2*sqrt(n)).  The author of the sequence also
authored the reference which contains the sequence:

1,1,2,1,1,1,4,2,1,6,1,1,11,4,2,1,11,6,1,1,28,11,4,2,1,35,11,
6,1,1,65,28,11,4,2,1,73,35,11,6,1,1,147,65,28,11,4,2,1,182,
73,35,11,6,1,1,321,147,65,28,11,4,2,1,374,182,73,35,11,6,1,
1,678,321,147,65,28,11,4,2,1


If you break the sequence up into runs of lengths 1, 1, 2, 2,
3, 3, and so a pattern emerges.

1
1
2,1
1,1
4,2,1
6,1,1
11,4,2,1
11,6,1,1
28,11,4,2,1
35,11,6,1,1
etc.

The runs are reversed initial segments of the two sequences

A100092(n^2-n+1) = (1,2,4,11,28,65,147,321,...)
A100092(n^2+1)   = (1,1,6,11,35,73,182,374,...)

These latter sequences are interesting in themselves, and
extended versions of them, as well as of A100092, appear on
page 3 or the reference.

I think the additional sequences should be included in the OEIS
as well.  I was unable to pick out formulae for the latter
sequences from the reference, maybe a seqfan could help.