A211550 - OEIS

%I #4 Apr 15 2012 11:10:21

%S 150,330,640,1190,2172,3922,7052,12734,22944,41816,76046,140318,

%T 258302,482748,900018,1702150,3211388,6136202,11697780,22541648,

%U 43345282,84091266,162828522,317556046,618284124,1210700090,2367405022,4650241676

%N Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and 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="/A211550/b211550.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +6*a(n-2) -66*a(n-3) +32*a(n-4) +343*a(n-5) -396*a(n-6) -874*a(n-7) +1475*a(n-8) +1066*a(n-9) -2702*a(n-10) -373*a(n-11) +2577*a(n-12) -367*a(n-13) -1195*a(n-14) +320*a(n-15) +210*a(n-16) -60*a(n-17)

%e Some solutions for n=3

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

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

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

%e ..0.-2..0.-4...-6..3..0..6...-2.-2.-2..3...-3.-3.-3..2...-2.-5.-2.-5

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 15 2012