Different squares on an n X n lattice

[Hugo Pfoertner]

Seqfans, Neil,

yesterday I had submitted the new sequence

http://www.research.att.com/projects/OEIS?Anum=A108279

(Neil, please keep it, ignoring my request sent by personal E-mail)

%S A108279
1,3,5,8,11,15,18,23,28,33,38,45,51,58,65,73,80,89,97,107,116,126,134,
%T A108279 146,158,169
%N A108279 Number of different sizes occurring among the
A002415(n)=n^2*(n^2-1)/12 squares that can be drawn using points of an n
X n square array as corners.
%H A108279 H. Bottomley, <a
href="http://www.research.att.com/~njas/sequences/a2415.gif">Illustration
of initial terms of A002415</a>
%e A108279 a(3)=3 because the 6 different squares that can be drawn on a
3X3 square lattice come in 3 sizes:
%e A108279 4 squares of side length 1:
%e A108279 x.x.o....o.x.x....o.o.o....o.o.o
%e A108279 x.x.o....o.x.x....x.x.o....o.x.x
%e A108279 o.o.o....o.o.o....x.x.o....o.x.x
%e A108279 1 square of side length sqrt(2):
%e A108279 o.x.o
%e A108279 x.o.x
%e A108279 o.x.o
%e A108279 1 square of side length 2:
%e A108279 x.o.x
%e A108279 o.o.o
%e A108279 x.o.x
%e A108279 a(4)=5 because there are 5 different sizes of squares that
can be drawn using the points of a 4X4 square lattice:
%e A108279 x.x.o.o....o.x.o.o....x.o.x.o....o.x.o.o....x.o.o.x
%e A108279 x.x.o.o....x.o.x.o....o.o.o.o....o.o.o.x....o.o.o.o
%e A108279 o.o.o.o....o.x.o.o....x.o.x.o....x.o.o.o....o.o.o.o
%e A108279 o.o.o.o....o.o.o.o....o.o.o.o....o.o.x.o....x.o.o.x
%Y A108279 Cf. A002415 4-dimensional pyramidal numbers.
%K A108279 more,nonn,new
%O A108279 2,2

In a hasty over-reaction to a comment my German friend Rainer Rosenthal
made in a discussion in the German mathematical newsgroup in a thread on
square-avoiding lattice colorings I had asked Neil to cancel this
sequence, because there was a deviation from Rainer's results starting
at a(8)=18 (he suggested a(8)=19). In the meantime I've checked my
program and couldn't find an error.

The source code is at
http://www.randomwalk.de/scimath/nxncol.for

Can someone here try to check at least the correctness of a(8)=18?

Thanks

Hugo Pfoertner