A211472 - OEIS

%I #4 Apr 12 2012 06:37:53

%S 121,873,6225,44205,312209,2195485,15376453,107305341,746401305,

%T 5176610637,35805913289,247058995669,1700863663801,11685223911345,

%U 80125271642765,548435823880377,3747645664538313,25569088975353613

%N Number of (n+1)X(n+1) -8..8 symmetric matrices with every 2X2 subblock having sum zero and one, three or four distinct values

%C Symmetry and 2X2 block sums zero implies that the diagonal x(i,i) are equal modulo 2 and x(i,j)=(x(i,i)+x(j,j))/2*(-1)^(i-j)

%H R. H. Hardin, <a href="/A211472/b211472.txt">Table of n, a(n) for n = 1..31</a>

%e Some solutions for n=3

%e .-1..4.-1.-2....2.-3..2.-4....0..1.-2..4....0.-4.-2.-3...-4..2..0..1

%e ..4.-7..4.-1...-3..4.-3..5....1.-2..3.-5...-4..8.-2..7....2..0.-2..1

%e .-1..4.-1.-2....2.-3..2.-4...-2..3.-4..6...-2.-2.-4.-1....0.-2..4.-3

%e .-2.-1.-2..5...-4..5.-4..6....4.-5..6.-8...-3..7.-1..6....1..1.-3..2

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 12 2012