A211553 Number of (n+1)X(n+1) -9..9 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values

181, 521, 1239, 2865, 6321, 14009, 30379, 66865, 145437, 322009, 708509, 1586445, 3542267, 8034795, 18210199, 41826241, 96089585, 223154883, 518575357, 1215390177, 2850562247, 6729628421, 15897536413, 37742249421, 89649505903

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) = 7*a(n-1) +14*a(n-2) -200*a(n-3) +78*a(n-4) +2555*a(n-5) -3384*a(n-6) -19202*a(n-7) +37730*a(n-8) +93668*a(n-9) -243670*a(n-10) -306260*a(n-11) +1060307*a(n-12) +654137*a(n-13) -3306120*a(n-14) -762798*a(n-15) +7617393*a(n-16) -164785*a(n-17) -13171236*a(n-18) +2551794*a(n-19) +17194836*a(n-20) -5381852*a(n-21) -16929450*a(n-22) +6682460*a(n-23) +12476338*a(n-24) -5590892*a(n-25) -6783218*a(n-26) +3249146*a(n-27) +2657689*a(n-28) -1305530*a(n-29) -723096*a(n-30) +352500*a(n-31) +128470*a(n-32) -60348*a(n-33) -13280*a(n-34) +5840*a(n-35) +600*a(n-36) -240*a(n-37)

Example

Some solutions for n=3
.-9..3.-8..4....7.-5..1.-3....4..1..4..1....1..1..1..3....0.-2.-2.-2
..3..3..2..2...-5..3..1..1....1.-6..1.-6....1.-3..1.-5...-2..4..0..4
.-8..2.-7..3....1..1.-5..3....4..1..4..1....1..1..1..3...-2..0.-4..0
..4..2..3..1...-3..1..3.-1....1.-6..1.-6....3.-5..3.-7...-2..4..0..4

Crossrefs

Sequence in context: A113156 A142391 A142552 * A253821 A154628 A142731

Adjacent sequences: A211550 A211551 A211552 * A211554 A211555 A211556

Keyword

nonn

Author

R. H. Hardin Apr 15 2012

Status

approved