A211115 Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and two or three distinct values.

12, 26, 54, 106, 208, 398, 766, 1458, 2792, 5324, 10206, 19550, 37616, 72446, 140048, 271194, 526792, 1025268, 2000636, 3911284, 7663264, 15040266, 29571962, 58231566, 114837690, 226761020, 448318274, 887305854, 1757921506, 3485905204

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) = 5*a(n-1) - 4*a(n-2) - 16*a(n-3) + 27*a(n-4) + 8*a(n-5) - 35*a(n-6) + 10*a(n-7) + 10*a(n-8) - 4*a(n-9).

Empirical g.f.: 2*x*(6 - 17*x - 14*x^2 + 66*x^3 - 7*x^4 - 76*x^5 + 29*x^6 + 22*x^7 - 10*x^8) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 15 2018

Example

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

Crossrefs

Sequence in context: A105814 A297427 A357893 * A232936 A274897 A030736

Adjacent sequences: A211112 A211113 A211114 * A211116 A211117 A211118

Keyword

nonn

Author

R. H. Hardin, Apr 02 2012

Status

approved