A211444 Number of (n+1)X(n+1) -7..7 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values

112, 294, 656, 1404, 2890, 5896, 11792, 23678, 46864, 93614, 184790, 368876, 728858, 1457004, 2886784, 5784714, 11502262, 23114684, 46139666, 92997430, 186362182, 376728674, 757813990, 1536216028, 3101292166, 6303428906, 12767750824

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) +11*a(n-2) -89*a(n-3) -13*a(n-4) +684*a(n-5) -385*a(n-6) -2968*a(n-7) +2808*a(n-8) +7974*a(n-9) -9684*a(n-10) -13663*a(n-11) +19830*a(n-12) +14785*a(n-13) -25455*a(n-14) -9593*a(n-15) +20503*a(n-16) +3277*a(n-17) -10058*a(n-18) -372*a(n-19) +2842*a(n-20) -58*a(n-21) -416*a(n-22) +12*a(n-23) +24*a(n-24)

Example

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

Crossrefs

Sequence in context: A296579 A297970 A296185 * A270759 A352585 A233892

Adjacent sequences: A211441 A211442 A211443 * A211445 A211446 A211447

Keyword

nonn

Author

R. H. Hardin Apr 11 2012

Status

approved