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A211712
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Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values
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1
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231, 537, 1099, 2099, 3997, 7379, 13747, 25335, 47093, 87513, 163699, 307721, 581223, 1105495, 2109715, 4055319, 7812709, 15150193, 29420803, 57448799, 112272663, 220389539, 432816337, 852950837, 1681246791, 3322791067
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OFFSET
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1,1
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COMMENTS
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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)
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LINKS
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FORMULA
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Empirical: a(n) = 5*a(n-1) +9*a(n-2) -80*a(n-3) +9*a(n-4) +535*a(n-5) -425*a(n-6) -1941*a(n-7) +2321*a(n-8) +4142*a(n-9) -6337*a(n-10) -5243*a(n-11) +10073*a(n-12) +3703*a(n-13) -9603*a(n-14) -1139*a(n-15) +5360*a(n-16) -87*a(n-17) -1632*a(n-18) +123*a(n-19) +238*a(n-20) -18*a(n-21) -12*a(n-22)
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EXAMPLE
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Some solutions for n=3
..3..0..3..0....5.-1.-3.-1...-1..3..1..0....1..3..2..3...10.-6.10.-2
..0.-3..0.-3...-1.-3..7.-3....3.-5..1.-2....3.-7..2.-7...-6..2.-6.-2
..3..0..3..0...-3..7-11..7....1..1..3.-2....2..2..3..2...10.-6.10.-2
..0.-3..0.-3...-1.-3..7.-3....0.-2.-2..1....3.-7..2.-7...-2.-2.-2.-6
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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