A211550 Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and three distinct values

150, 330, 640, 1190, 2172, 3922, 7052, 12734, 22944, 41816, 76046, 140318, 258302, 482748, 900018, 1702150, 3211388, 6136202, 11697780, 22541648, 43345282, 84091266, 162828522, 317556046, 618284124, 1210700090, 2367405022, 4650241676

Offset

1,1

Comments

Symmetry and 2X2 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) = 5*a(n-1) +6*a(n-2) -66*a(n-3) +32*a(n-4) +343*a(n-5) -396*a(n-6) -874*a(n-7) +1475*a(n-8) +1066*a(n-9) -2702*a(n-10) -373*a(n-11) +2577*a(n-12) -367*a(n-13) -1195*a(n-14) +320*a(n-15) +210*a(n-16) -60*a(n-17)

Example

Some solutions for n=3
..4.-2..4..0....6.-3..0.-6....1..3..1.-2....4..2..4.-3....9.-2..9.-2
.-2..0.-2.-2...-3..0..3..3....3.-7..3.-2....2.-8..2.-3...-2.-5.-2.-5
..4.-2..4..0....0..3.-6..0....1..3..1.-2....4..2..4.-3....9.-2..9.-2
..0.-2..0.-4...-6..3..0..6...-2.-2.-2..3...-3.-3.-3..2...-2.-5.-2.-5

Crossrefs

Sequence in context: A063829 A291959 A210643 * A212465 A273322 A206066

Adjacent sequences: A211547 A211548 A211549 * A211551 A211552 A211553

Keyword

nonn

Author

R. H. Hardin Apr 15 2012

Status

approved