A211710 Number of (n+1) X (n+1) -11..11 symmetric matrices with every 2 X 2 subblock having sum zero and two distinct values.

34, 46, 64, 94, 142, 220, 346, 550, 880, 1414, 2278, 3676, 5938, 9598, 15520, 25102, 40606, 65692, 106282, 171958, 278224, 450166, 728374, 1178524, 1906882, 3085390, 4992256, 8077630, 13069870, 21147484, 34217338, 55364806, 89582128, 144946918

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..165

Formula

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

Empirical g.f.: 2*x*(17 - 11*x - 14*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 19 2018

Example

Some solutions for n=3:
.-3.-3.-3..3....2.-2..2.-2...-6..2.-2..2....1.-1..1..1....1.-1.-1.-1
.-3..9.-3..3...-2..2.-2..2....2..2.-2..2...-1..1.-1.-1...-1..1..1..1
.-3.-3.-3..3....2.-2..2.-2...-2.-2..2.-2....1.-1..1..1...-1..1.-3..1
..3..3..3.-3...-2..2.-2..2....2..2.-2..2....1.-1..1.-3...-1..1..1..1

Crossrefs

Sequence in context: A341173 A352787 A074757 * A039327 A043150 A043930

Adjacent sequences: A211707 A211708 A211709 * A211711 A211712 A211713

Keyword

nonn

Author

R. H. Hardin, Apr 20 2012

Status

approved