A211253 Number of (n+1) X (n+1) -6..6 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.

21, 29, 41, 61, 93, 145, 229, 365, 585, 941, 1517, 2449, 3957, 6397, 10345, 16733, 27069, 43793, 70853, 114637, 185481, 300109, 485581, 785681, 1271253, 2056925, 3328169, 5385085, 8713245, 14098321, 22811557, 36909869, 59721417, 96631277

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*(21 - 13*x - 17*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 16 2018

Example

Some solutions for n=3:
.-1.-1.-1.-1...-3..1.-1..3....3.-1..1.-3....2.-2..2..2...-1..1..1..1
.-1..3.-1..3....1..1.-1.-1...-1.-1..1..1...-2..2.-2.-2....1.-1.-1.-1
.-1.-1.-1.-1...-1.-1..1..1....1..1.-1.-1....2.-2..2..2....1.-1..3.-1
.-1..3.-1..3....3.-1..1.-3...-3..1.-1..3....2.-2..2.-6....1.-1.-1.-1

Crossrefs

Sequence in context: A166647 A119107 A004196 * A209975 A077787 A039372

Adjacent sequences: A211250 A211251 A211252 * A211254 A211255 A211256

Keyword

nonn

Author

R. H. Hardin, Apr 06 2012

Status

approved