%I #4 Apr 15 2012 11:11:54
%S 180,504,1148,2508,5202,10762,21622,43984,87406,177030,351096,711810,
%T 1414930,2878790,5747458,11748876,23580200,48449984,97774376,
%U 201923574,409657252,850120676,1733171824,3612646782,7397620764,15481145862
%N Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and two or three 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="/A211552/b211552.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) +17*a(n-2) -166*a(n-3) -31*a(n-4) +2043*a(n-5) -1600*a(n-6) -14704*a(n-7) +20269*a(n-8) +68225*a(n-9) -129342*a(n-10) -210658*a(n-11) +529848*a(n-12) +422669*a(n-13) -1504565*a(n-14) -469508*a(n-15) +3056859*a(n-16) -21015*a(n-17) -4491182*a(n-18) +1054426*a(n-19) +4754701*a(n-20) -1955055*a(n-21) -3565976*a(n-22) +2006020*a(n-23) +1829375*a(n-24) -1309433*a(n-25) -598506*a(n-26) +551716*a(n-27) +104454*a(n-28) -144434*a(n-29) -2452*a(n-30) +21200*a(n-31) -2120*a(n-32) -1320*a(n-33) +240*a(n-34)
%e Some solutions for n=3
%e ..1..1..1..2....1.-1.-1.-1....8..0..0..0...-1..2.-1..2...-6..2.-3..2
%e ..1.-3..1.-4...-1..1..1..1....0.-8..8.-8....2.-3..2.-3....2..2.-1..2
%e ..1..1..1..2...-1..1.-3..1....0..8.-8..8...-1..2.-1..2...-3.-1..0.-1
%e ..2.-4..2.-5...-1..1..1..1....0.-8..8.-8....2.-3..2.-3....2..2.-1..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 15 2012