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A211554 Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and three or four distinct values 1

%I #4 Apr 15 2012 11:13:25

%S 150,1194,9390,73506,572242,4435846,34254414,263666834,2023872594,

%T 15497836998,118429480822,903378800274,6880209099890,52328684259574,

%U 397516660098150,3016531736769506,22869029384939666,173227696174568614

%N Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and 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="/A211554/b211554.txt">Table of n, a(n) for n = 1..25</a>

%e Some solutions for n=3

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

%e .-3..8.-5..7....5.-6..7.-3....2.-9..6.-2....5.-8..5.-4...-6..3.-6.-1

%e ..0.-5..2.-4...-6..7.-8..4....1..6.-3.-1...-2..5.-2..1....9.-6..9.-2

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 15 2012

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