OFFSET
1,1
COMMENTS
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).
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 2*a(n-1) - a(n-3).
Conjectures from Colin Barker, Jul 18 2018: (Start)
G.f.: x*(13 - 9*x - 11*x^2) / ((1 - x)*(1 - x - x^2)).
a(n) = 7 + (2^(1-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).
(End)
EXAMPLE
Some solutions for n=3:
.-2..2.-2..2....0..0..0..0....1.-1.-1.-1....4.-4..4.-4...-3..1.-1..3
..2.-2..2.-2....0..0..0..0...-1..1..1..1...-4..4.-4..4....1..1.-1.-1
.-2..2.-2..2....0..0..0..0...-1..1.-3..1....4.-4..4.-4...-1.-1..1..1
..2.-2..2.-2....0..0..0..0...-1..1..1..1...-4..4.-4..4....3.-1..1.-3
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 13 2012
STATUS
approved