A211814 Number of (n+1)X(n+1) -10..10 symmetric matrices with every 2X2 subblock having sum zero and three distinct values

188, 414, 812, 1510, 2778, 5014, 9064, 16350, 29566, 53808, 98098, 180732, 333300, 622046, 1161392, 2193998, 4144530, 7912796, 15101998, 29086670, 55991176, 108595704, 210489002, 410470320, 799923628, 1566429434, 3065502158

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) = 6*a(n-1) +2*a(n-2) -77*a(n-3) +93*a(n-4) +372*a(n-5) -775*a(n-6) -766*a(n-7) +2711*a(n-8) +230*a(n-9) -4967*a(n-10) +1748*a(n-11) +4882*a(n-12) -3055*a(n-13) -2382*a(n-14) +2083*a(n-15) +433*a(n-16) -619*a(n-17) +28*a(n-18) +66*a(n-19) -12*a(n-20)

Example

Some solutions for n=3
.-6..5.-4..5...-4..1.-4..7....0.-1.-1.-1...-7..4.-7..4...-2..4.-6..4
..5.-4..3.-4....1..2..1.-4...-1..2..0..2....4.-1..4.-1....4.-6..8.-6
.-4..3.-2..3...-4..1.-4..7...-1..0.-2..0...-7..4.-7..4...-6..8-10..8
..5.-4..3.-4....7.-4..7-10...-1..2..0..2....4.-1..4.-1....4.-6..8.-6

Crossrefs

Sequence in context: A260836 A304279 A099945 * A335592 A233786 A233961

Adjacent sequences: A211811 A211812 A211813 * A211815 A211816 A211817

Keyword

nonn

Author

R. H. Hardin Apr 21 2012

Status

approved