A211257 Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values

85, 231, 547, 1283, 2901, 6595, 14775, 33409, 75157, 170723, 387687, 888293, 2039449, 4718583, 10949039, 25566565, 59877913, 140930679, 332585711, 787830185, 1870341077, 4452666039, 10618825855, 25375634725, 60720707925

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) +6*a(n-2) -97*a(n-3) +62*a(n-4) +668*a(n-5) -852*a(n-6) -2556*a(n-7) +4359*a(n-8) +5935*a(n-9) -12593*a(n-10) -8545*a(n-11) +22727*a(n-12) +7400*a(n-13) -26431*a(n-14) -3396*a(n-15) +19783*a(n-16) +389*a(n-17) -9298*a(n-18) +302*a(n-19) +2606*a(n-20) -118*a(n-21) -392*a(n-22) +12*a(n-23) +24*a(n-24)

Example

Some solutions for n=3
..3.-2..1.-2...-4..2.-2..1....4..0..0..0...-2..1.-1..2....3.-1..2.-1
.-2..1..0..1....2..0..0..1....0.-4..4.-4....1..0..0.-1...-1.-1..0.-1
..1..0.-1..0...-2..0..0.-1....0..4.-4..4...-1..0..0..1....2..0..1..0
.-2..1..0..1....1..1.-1..2....0.-4..4.-4....2.-1..1.-2...-1.-1..0.-1

Crossrefs

Sequence in context: A044798 A260100 A072289 * A027524 A043340 A045129

Adjacent sequences: A211254 A211255 A211256 * A211258 A211259 A211260

Keyword

nonn

Author

R. H. Hardin Apr 06 2012

Status

approved