A211328 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and two, three or four distinct values.

24, 86, 310, 1134, 4190, 15582, 58130, 217014, 809418, 3013130, 11188738, 41433570, 153004862, 563461506, 2069583806, 7582810302, 27719202126, 101113824446, 368123385634, 1337824919574, 4853929237946, 17584750606794, 63618436617746

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..90

Formula

Empirical: a(n) = 13*a(n-1) - 63*a(n-2) + 130*a(n-3) - 65*a(n-4) - 115*a(n-5) + 69*a(n-6) + 68*a(n-7) + 12*a(n-8).

Empirical g.f.: 2*x*(12 - 113*x + 352*x^2 - 299*x^3 - 321*x^4 + 302*x^5 + 249*x^6 + 42*x^7) / ((1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)*(1 - 3*x - x^2)*(1 - 3*x - 2*x^2)). - Colin Barker, Jul 17 2018

Example

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

Crossrefs

Sequence in context: A168538 A007201 A228874 * A304375 A044211 A044592

Adjacent sequences: A211325 A211326 A211327 * A211329 A211330 A211331

Keyword

nonn

Author

R. H. Hardin, Apr 07 2012

Status

approved