A211445 Number of (n+1)X(n+1) -7..7 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values

113, 307, 723, 1659, 3681, 8171, 17905, 39605, 87221, 194399, 433363, 977621, 2211117, 5053989, 11592995, 26825177, 62296037, 145661855, 341690587, 805669229, 1904747123, 4520182115, 10749370491, 25632216197, 61218130049

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) +9*a(n-2) -114*a(n-3) +38*a(n-4) +953*a(n-5) -941*a(n-6) -4622*a(n-7) +6247*a(n-8) +14455*a(n-9) -23114*a(n-10) -30709*a(n-11) +54571*a(n-12) +45628*a(n-13) -86067*a(n-14) -48323*a(n-15) +91676*a(n-16) +37008*a(n-17) -65251*a(n-18) -20648*a(n-19) +30111*a(n-20) +8274*a(n-21) -8512*a(n-22) -2240*a(n-23) +1318*a(n-24) +356*a(n-25) -84*a(n-26) -24*a(n-27)

Example

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

Crossrefs

Sequence in context: A051110 A031932 A216310 * A172983 A358034 A069794

Adjacent sequences: A211442 A211443 A211444 * A211446 A211447 A211448

Keyword

nonn

Author

R. H. Hardin Apr 11 2012

Status

approved