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.

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

R. H. Hardin, Table of n, a(n) for n = 1..192

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

Adjacent sequences: A211546 A211547 A211548 * A211550 A211551 A211552

Keyword

nonn

Author

R. H. Hardin, Apr 15 2012

Status

approved