A211712 Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values

231, 537, 1099, 2099, 3997, 7379, 13747, 25335, 47093, 87513, 163699, 307721, 581223, 1105495, 2109715, 4055319, 7812709, 15150193, 29420803, 57448799, 112272663, 220389539, 432816337, 852950837, 1681246791, 3322791067

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) +9*a(n-2) -80*a(n-3) +9*a(n-4) +535*a(n-5) -425*a(n-6) -1941*a(n-7) +2321*a(n-8) +4142*a(n-9) -6337*a(n-10) -5243*a(n-11) +10073*a(n-12) +3703*a(n-13) -9603*a(n-14) -1139*a(n-15) +5360*a(n-16) -87*a(n-17) -1632*a(n-18) +123*a(n-19) +238*a(n-20) -18*a(n-21) -12*a(n-22)

Example

Some solutions for n=3
..3..0..3..0....5.-1.-3.-1...-1..3..1..0....1..3..2..3...10.-6.10.-2
..0.-3..0.-3...-1.-3..7.-3....3.-5..1.-2....3.-7..2.-7...-6..2.-6.-2
..3..0..3..0...-3..7-11..7....1..1..3.-2....2..2..3..2...10.-6.10.-2
..0.-3..0.-3...-1.-3..7.-3....0.-2.-2..1....3.-7..2.-7...-2.-2.-2.-6

Crossrefs

Sequence in context: A337231 A117223 A160355 * A324315 A276832 A324319

Adjacent sequences: A211709 A211710 A211711 * A211713 A211714 A211715

Keyword

nonn

Author

R. H. Hardin Apr 20 2012

Status

approved