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A211549
Number of (n+1) X (n+1) -9..9 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
1
31, 43, 61, 91, 139, 217, 343, 547, 877, 1411, 2275, 3673, 5935, 9595, 15517, 25099, 40603, 65689, 106279, 171955, 278221, 450163, 728371, 1178521, 1906879, 3085387, 4992253, 8077627, 13069867, 21147481, 34217335, 55364803, 89582125, 144946915
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
FORMULA
Empirical: a(n) = 2*a(n-1) - a(n-3).
Empirical g.f.: x*(31 - 19*x - 25*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 19 2018
EXAMPLE
Some solutions for n=3:
..9.-3..3.-9....3.-3..3.-3...-1.-1.-1..1....7.-7..7.-7....2.-2..2.-2
.-3.-3..3..3...-3..3.-3..3...-1..3.-1..1...-7..7.-7..7...-2..2.-2..2
..3..3.-3.-3....3.-3..3.-3...-1.-1.-1..1....7.-7..7.-7....2.-2..2.-2
.-9..3.-3..9...-3..3.-3..3....1..1..1.-1...-7..7.-7..7...-2..2.-2..2
CROSSREFS
Sequence in context: A317851 A304239 A069455 * A118637 A096163 A139883
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 15 2012
STATUS
approved