A211467 - OEIS

%I #4 Apr 12 2012 06:33:06

%S 120,260,508,940,1734,3126,5690,10276,18758,34230,63068,116594,217310,

%T 407026,767450,1454628,2771646,5306940,10202586,19697838,38146332,

%U 74135060,144403432,282088738,551970304,1082582606,2125859552,4182450010

%N Number of (n+1)X(n+1) -8..8 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="/A211467/b211467.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +9*a(n-2) -52*a(n-3) -16*a(n-4) +271*a(n-5) -86*a(n-6) -724*a(n-7) +435*a(n-8) +1052*a(n-9) -760*a(n-10) -817*a(n-11) +575*a(n-12) +320*a(n-13) -150*a(n-14) -60*a(n-15)

%e Some solutions for n=3

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

%e ..0.-1..0.-1...-4..6.-1..6...-1.-3.-1.-2....2.-8..4.-8....0.-2..1.-2

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

%e ..0.-1..0.-1...-4..6.-1..6...-2.-2.-2.-1....2.-8..4.-8....0.-2..1.-2

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 12 2012