A211323 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values.

14, 24, 42, 76, 140, 262, 496, 948, 1826, 3540, 6900, 13510, 26552, 52348, 103474, 204972, 406748, 808326, 1608288, 3203044, 6384194, 12732964, 25408612, 50724486, 101298920, 202355052, 404317266, 807998908, 1614969356, 3228274630

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) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).

Empirical g.f.: 2*x*(7 - 16*x + x^2 + 9*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Jul 16 2018

Example

Some solutions for n=3.
..3..0..3..0....2.-1..0.-2....0.-1.-1..0....1.-2..1.-2....2.-1..0.-1
..0.-3..0.-3...-1..0..1..1...-1..2..0..1...-2..3.-2..3...-1..0..1..0
..3..0..3..0....0..1.-2..0...-1..0.-2..1....1.-2..1.-2....0..1.-2..1
..0.-3..0.-3...-2..1..0..2....0..1..1..0...-2..3.-2..3...-1..0..1..0

Crossrefs

Sequence in context: A111743 A164399 A164404 * A141838 A140499 A068365

Adjacent sequences: A211320 A211321 A211322 * A211324 A211325 A211326

Keyword

nonn

Author

R. H. Hardin, Apr 07 2012

Status

approved