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Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values
1

%I #4 Apr 07 2012 19:42:31

%S 60,332,1846,10332,58164,329130,1870664,10670876,61044918,349974788,

%T 2009495068,11549465226,66414142512,381959562756,2196335839046,

%U 12624063953180,72516570941316,416247502883594,2387248114517560

%N Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and two, 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="/A211336/b211336.txt">Table of n, a(n) for n = 1..74</a>

%F Empirical: a(n) = 32*a(n-1) -429*a(n-2) +3078*a(n-3) -12340*a(n-4) +24890*a(n-5) -10895*a(n-6) -35870*a(n-7) +19131*a(n-8) +40338*a(n-9) +18694*a(n-10) +3532*a(n-11) +240*a(n-12)

%e Some solutions for n=3

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 07 2012