conference matrices

[Joerg Arndt]

Wikipedia is your friend:

http://en.wikipedia.org/wiki/Conference_matrix

If C is a symmetric conference matrix of order n > 1, then not only
must n be congruent to 2 (mod 4) but also n − 1 must be a sum of two
square integers.

So we may want to change the definition of the sequence.

... and add the 3 mod 4 prime-power case to the OEIS:
Antisymmetric conference matrices can also be produced by the Paley
construction. Let q be a prime power with residue 3 (mod 4). [etc.]

cheers,   jj


* Joerg Arndt <arndt at jjj.de> [Mar 14. 2008 09:06]:
> 
> Why is sequence A000952 restricted to 2 mod 4?
> 
> For the record:
> 
> ---- snip ----
> The conference matrices obtained are of size $c=q^n+1$ where $q$ is an odd prime.
> The values $c\leq{}100$ are:
>     4, 6, 8, 10, 12, 14, 18, 20, 24, 26, 28, 30, 32, 38, 42, 44, 48,
>     50, 54, 60, 62, 68, 72, 74, 80, 82, 84, 90, 98
> ---- snip ----
> (cd. A061344)
> and
> ---- snip ----
> We do not obtain conference matrices for any odd $c$ and these even
> values $c\leq{}100$:
>     2, 16, 22, 34, 36, 40, 46, 52, 56, 58, 64, 66, 70, 76, 78, 86, 88, 92, 94, 96, 100
> For example, $c=16=15+1=3\cdot{}5+1$ has not the required form.
> ---- snip ----
> 
> regards,   jj
> 



Dear JJ

You said:

Why is sequence A000952 restricted to 2 mod 4?

full set of N 's such that a c. mx. exists!

i agree that for this
condotion is automatically satidfied