A211117 Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and two, three or four distinct values.

12, 30, 72, 174, 422, 1028, 2510, 6134, 14988, 36594, 89250, 217416, 529010, 1285754, 3121904, 7573550, 18358950, 44474532, 107679342, 260584230, 630363356, 1524363938, 3685232642, 8907169352, 21524344338, 52005554058, 125635087296

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) = 6*a(n-1) - 11*a(n-2) + 3*a(n-3) + 8*a(n-4) - 3*a(n-5) - 2*a(n-6).

Empirical g.f.: 2*x*(6 - 21*x + 12*x^2 + 18*x^3 - 8*x^4 - 5*x^5) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x - x^2)). - Colin Barker, Jul 16 2018

Example

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

Crossrefs

Sequence in context: A334791 A110019 A069486 * A301775 A175157 A371075

Adjacent sequences: A211114 A211115 A211116 * A211118 A211119 A211120

Keyword

nonn

Author

R. H. Hardin, Apr 02 2012

Status

approved