A211114 Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values.

9, 19, 39, 81, 167, 341, 695, 1405, 2839, 5709, 11479, 23021, 46167, 92461, 185175, 370605, 741719, 1483949, 2968919, 5938861, 11879767, 23761581, 47527255, 95058605, 190125399, 380258989, 760534359, 1521085101, 3042202967, 6084438701

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

Empirical g.f.: x*(9 + x - 26*x^2 + 20*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 2*x^2)). - Colin Barker, Jul 15 2018

Example

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

Crossrefs

Sequence in context: A145958 A290245 A039299 * A159697 A014005 A286624

Adjacent sequences: A211111 A211112 A211113 * A211115 A211116 A211117

Keyword

nonn

Author

R. H. Hardin, Apr 02 2012

Status

approved