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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 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin Apr 15 2012
STATUS
approved

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Last modified May 24 11:32 EDT 2024. Contains 372773 sequences. (Running on oeis4.)