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Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values
1

%I #4 Apr 06 2012 10:59:00

%S 65,143,287,567,1109,2145,4163,8041,15609,30271,58955,114925,224757,

%T 440281,864529,1700629,3351109,6614459,13071953,25871279,51248961,

%U 101644005,201725287,400751925,796518335,1584431751,3152835011

%N Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and one 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="/A211255/b211255.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +5*a(n-2) -36*a(n-3) +5*a(n-4) +123*a(n-5) -69*a(n-6) -205*a(n-7) +150*a(n-8) +176*a(n-9) -138*a(n-10) -74*a(n-11) +56*a(n-12) +12*a(n-13) -8*a(n-14)

%e Some solutions for n=3

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 06 2012