A211329 Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.

15, 19, 25, 35, 51, 77, 119, 187, 297, 475, 763, 1229, 1983, 3203, 5177, 8371, 13539, 21901, 35431, 57323, 92745, 150059, 242795, 392845, 635631, 1028467, 1664089, 2692547, 4356627, 7049165, 11405783, 18454939, 29860713, 48315643, 78176347

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) - a(n-3).

Empirical g.f.: x*(15 - 11*x - 13*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 17 2018

Example

Some solutions for n=3:
.-1..1.-1.-1....4.-4..4.-4....1..1..1.-1....1.-1..1..1...-2..2.-2..2
..1.-1..1..1...-4..4.-4..4....1.-3..1.-1...-1..1.-1.-1....2.-2..2.-2
.-1..1.-1.-1....4.-4..4.-4....1..1..1.-1....1.-1..1..1...-2..2.-2..2
.-1..1.-1..3...-4..4.-4..4...-1.-1.-1..1....1.-1..1.-3....2.-2..2.-2

Crossrefs

Sequence in context: A257020 A234849 A164564 * A104298 A032475 A169728

Adjacent sequences: A211326 A211327 A211328 * A211330 A211331 A211332

Keyword

nonn

Author

R. H. Hardin, Apr 07 2012

Status

approved