A211443 Number of (n+1)X(n+1) -7..7 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values

91, 201, 397, 765, 1459, 2751, 5215, 9855, 18759, 35741, 68529, 131739, 254515, 493209, 959339, 1871379, 3660547, 7178105, 14104015, 27769453, 54754733, 108142387, 213809725, 423287363, 838643733, 1663340421, 3300898801

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) = 3*a(n-1) +9*a(n-2) -31*a(n-3) -30*a(n-4) +125*a(n-5) +48*a(n-6) -251*a(n-7) -46*a(n-8) +264*a(n-9) +40*a(n-10) -138*a(n-11) -28*a(n-12) +28*a(n-13) +8*a(n-14)

Example

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

Crossrefs

Sequence in context: A352133 A044423 A044804 * A305761 A339523 A260064

Adjacent sequences: A211440 A211441 A211442 * A211444 A211445 A211446

Keyword

nonn

Author

R. H. Hardin Apr 11 2012

Status

approved