A211322 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.

11, 15, 21, 31, 47, 73, 115, 183, 293, 471, 759, 1225, 1979, 3199, 5173, 8367, 13535, 21897, 35427, 57319, 92741, 150055, 242791, 392841, 635627, 1028463, 1664085, 2692543, 4356623, 7049161, 11405779, 18454935, 29860709, 48315639, 78176343

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 16 2018: (Start)

G.f.: x*(11 - 7*x - 9*x^2) / ((1 - x)*(1 - x - x^2)).

a(n) = 5 + (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:
.-1.-1.-1..1...-1..1.-1.-1....0..0..0..0...-3..1.-3..1....3.-3..3.-3
.-1..3.-1..1....1.-1..1..1....0..0..0..0....1..1..1..1...-3..3.-3..3
.-1.-1.-1..1...-1..1.-1.-1....0..0..0..0...-3..1.-3..1....3.-3..3.-3
..1..1..1.-1...-1..1.-1..3....0..0..0..0....1..1..1..1...-3..3.-3..3

Crossrefs

Sequence in context: A237278 A265114 A213179 * A087682 A104628 A045564

Adjacent sequences: A211319 A211320 A211321 * A211323 A211324 A211325

Keyword

nonn

Author

R. H. Hardin, Apr 07 2012

Status

approved