A211324 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values.

15, 29, 55, 107, 209, 409, 805, 1583, 3127, 6175, 12233, 24241, 48141, 95655, 190343, 378967, 755249, 1505841, 3004341, 5996175, 11972503, 23911631, 47770041, 95451441, 190761021, 381287447, 762198439, 1523777639, 3046559585, 6091487857

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) = 3*a(n-1) + 2*a(n-2) - 11*a(n-3) + a(n-4) + 12*a(n-5) - 2*a(n-6) - 4*a(n-7).

Empirical g.f.: x*(15 - 16*x - 62*x^2 + 49*x^3 + 82*x^4 - 36*x^5 - 36*x^6) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)). - Colin Barker, Jul 16 2018

Example

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

Crossrefs

Sequence in context: A104811 A131877 A354161 * A354163 A146427 A202512

Adjacent sequences: A211321 A211322 A211323 * A211325 A211326 A211327

Keyword

nonn

Author

R. H. Hardin, Apr 07 2012

Status

approved