A211253 - OEIS

%I #8 Jul 16 2018 05:22:48

%S 21,29,41,61,93,145,229,365,585,941,1517,2449,3957,6397,10345,16733,

%T 27069,43793,70853,114637,185481,300109,485581,785681,1271253,2056925,

%U 3328169,5385085,8713245,14098321,22811557,36909869,59721417,96631277

%N Number of (n+1) X (n+1) -6..6 symmetric matrices with every 2 X 2 subblock having sum zero and one or two 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="/A211253/b211253.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-3).

%F Empirical g.f.: x*(21 - 13*x - 17*x^2) / ((1 - x)*(1 - x - x^2)). - _Colin Barker_, Jul 16 2018

%e Some solutions for n=3:

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

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

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

%e .-1..3.-1..3....3.-1..1.-3...-3..1.-1..3....2.-2..2.-6....1.-1.-1.-1

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 06 2012