A211256 Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values

84, 218, 482, 1036, 2134, 4382, 8810, 17818, 35538, 71522, 142458, 286522, 571602, 1151174, 2303198, 4648814, 9332754, 18885906, 38047946, 77198226, 156057706, 317451158, 643803786, 1312796154, 2670343286, 5457409302, 11131101682

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) = 4*a(n-1) +10*a(n-2) -56*a(n-3) -24*a(n-4) +321*a(n-5) -83*a(n-6) -968*a(n-7) +584*a(n-8) +1640*a(n-9) -1342*a(n-10) -1543*a(n-11) +1518*a(n-12) +750*a(n-13) -868*a(n-14) -166*a(n-15) +236*a(n-16) +12*a(n-17) -24*a(n-18)

Example

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

Crossrefs

Sequence in context: A181113 A254464 A135804 * A335081 A219808 A219459

Adjacent sequences: A211253 A211254 A211255 * A211257 A211258 A211259

Keyword

nonn

Author

R. H. Hardin Apr 06 2012

Status

approved