%I #4 Apr 20 2012 06:20:01

%S 264,726,1670,3574,7448,15136,30436,60938,120832,241150,476020,951586,

%T 1878928,3771022,7467440,15063942,29958046,60772582,121463624,

%U 247803532,497864910,1021347926,2062591634,4253485786,8631871242,17886996814

%N Number of (n+1)X(n+1) -11..11 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="/A211713/b211713.txt">Table of n, a(n) for n = 1..201</a>

%F Empirical: a(n) = 5*a(n-1) +23*a(n-2) -149*a(n-3) -196*a(n-4) +2007*a(n-5) +424*a(n-6) -16175*a(n-7) +5683*a(n-8) +87013*a(n-9) -61030*a(n-10) -330011*a(n-11) +313597*a(n-12) +908524*a(n-13) -1043207*a(n-14) -1841180*a(n-15) +2438675*a(n-16) +2754829*a(n-17) -4138459*a(n-18) -3021301*a(n-19) +5162035*a(n-20) +2381895*a(n-21) -4737637*a(n-22) -1297351*a(n-23) +3176171*a(n-24) +447161*a(n-25) -1532186*a(n-26) -72331*a(n-27) +519056*a(n-28) -8146*a(n-29) -118840*a(n-30) +6266*a(n-31) +17252*a(n-32) -1128*a(n-33) -1408*a(n-34) +72*a(n-35) +48*a(n-36)

%e Some solutions for n=3

%e .-3..0..0..6...-7..4.-1..4..-11..1.-5..1....6.-8..6.-8....2..2..2.-3

%e ..0..3.-3.-3....4.-1.-2.-1....1..9.-5..9...-8.10.-8.10....2.-6..2.-1

%e ..0.-3..3..3...-1.-2..5.-2...-5.-5..1.-5....6.-8..6.-8....2..2..2.-3

%e ..6.-3..3.-9....4.-1.-2.-1....1..9.-5..9...-8.10.-8.10...-3.-1.-3..4

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 20 2012