A211549 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A211549

Number of (n+1) X (n+1) -9..9 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.

31, 43, 61, 91, 139, 217, 343, 547, 877, 1411, 2275, 3673, 5935, 9595, 15517, 25099, 40603, 65689, 106279, 171955, 278221, 450163, 728371, 1178521, 1906879, 3085387, 4992253, 8077627, 13069867, 21147481, 34217335, 55364803, 89582125, 144946915

(list; graph; refs; listen; history; text; internal format)

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..192

FORMULA

Empirical: a(n) = 2*a(n-1) - a(n-3).

Empirical g.f.: x*(31 - 19*x - 25*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 19 2018

EXAMPLE

Some solutions for n=3:

..9.-3..3.-9....3.-3..3.-3...-1.-1.-1..1....7.-7..7.-7....2.-2..2.-2

.-3.-3..3..3...-3..3.-3..3...-1..3.-1..1...-7..7.-7..7...-2..2.-2..2

..3..3.-3.-3....3.-3..3.-3...-1.-1.-1..1....7.-7..7.-7....2.-2..2.-2

.-9..3.-3..9...-3..3.-3..3....1..1..1.-1...-7..7.-7..7...-2..2.-2..2

CROSSREFS

Sequence in context: A317851 A304239 A069455 * A118637 A096163 A139883

Adjacent sequences: A211546 A211547 A211548 * A211550 A211551 A211552

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 15 2012

STATUS

approved