A211326 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one, two or three distinct values.

25, 63, 149, 357, 829, 1941, 4479, 10413, 24087, 56079, 130523, 305431, 715961, 1685595, 3977689, 9418701, 22352933, 53188057, 126803131, 302898825, 724648975, 1736139523, 4164319291, 9999028263, 24029343133, 57789827919, 139068433021

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..203

Formula

Empirical: a(n) = 5*a(n-1) - a(n-2) - 29*a(n-3) + 33*a(n-4) + 50*a(n-5) - 88*a(n-6) - 14*a(n-7) + 73*a(n-8) - 22*a(n-9) - 10*a(n-10) + 4*a(n-11).

Empirical g.f.: x*(25 - 62*x - 141*x^2 + 400*x^3 + 195*x^4 - 855*x^5 + 89*x^6 + 663*x^7 - 248*x^8 - 102*x^9 + 44*x^10) / ((1 - x)*(1 - 2*x)*(1 + x - x^2)*(1 - 2*x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 16 2018

Example

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

Crossrefs

Sequence in context: A166873 A242317 A251688 * A103645 A061970 A159008

Adjacent sequences: A211323 A211324 A211325 * A211327 A211328 A211329

Keyword

nonn

Author

R. H. Hardin, Apr 07 2012

Status

approved