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) = a(n-1) + 4*a(n-2) - 2*a(n-3) - 4*a(n-4).
Conjectures from Colin Barker, Jul 17 2018: (Start)
G.f.: x*(15 + 18*x - 24*x^2 - 28*x^3) / ((1 + x)*(1 - 2*x)*(1 - 2*x^2)).
a(n) = (-9*2^(n/2) + 29*2^n + 1)/3 for n even.
a(n) = (-3*2^(n/2+3/2) + 29*2^n - 1)/3 for n odd.
(End)
EXAMPLE
Some solutions for n=3:
.-1..2..1..0....0.-1..0.-1...-2..1..0..1....1.-2..1.-2....0..0..0..0
..2.-3..0.-1...-1..2.-1..2....1..0.-1..0...-2..3.-2..3....0..0..0..0
..1..0..3.-2....0.-1..0.-1....0.-1..2.-1....1.-2..1.-2....0..0..0..0
..0.-1.-2..1...-1..2.-1..2....1..0.-1..0...-2..3.-2..3....0..0..0..0
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 07 2012
STATUS
approved