A211117 - OEIS

%I #8 Jul 16 2018 04:47:17

%S 12,30,72,174,422,1028,2510,6134,14988,36594,89250,217416,529010,

%T 1285754,3121904,7573550,18358950,44474532,107679342,260584230,

%U 630363356,1524363938,3685232642,8907169352,21524344338,52005554058,125635087296

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

%C Symmetry and 2 X 2 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="/A211117/b211117.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 3*a(n-3) + 8*a(n-4) - 3*a(n-5) - 2*a(n-6).

%F Empirical g.f.: 2*x*(6 - 21*x + 12*x^2 + 18*x^3 - 8*x^4 - 5*x^5) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x - x^2)). - _Colin Barker_, Jul 16 2018

%e Some solutions for n=3:

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 02 2012