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A211328
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Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and two, three or four distinct values.
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1
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24, 86, 310, 1134, 4190, 15582, 58130, 217014, 809418, 3013130, 11188738, 41433570, 153004862, 563461506, 2069583806, 7582810302, 27719202126, 101113824446, 368123385634, 1337824919574, 4853929237946, 17584750606794, 63618436617746
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OFFSET
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1,1
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COMMENTS
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Symmetry and 2 X 2 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) = 13*a(n-1) - 63*a(n-2) + 130*a(n-3) - 65*a(n-4) - 115*a(n-5) + 69*a(n-6) + 68*a(n-7) + 12*a(n-8).
Empirical g.f.: 2*x*(12 - 113*x + 352*x^2 - 299*x^3 - 321*x^4 + 302*x^5 + 249*x^6 + 42*x^7) / ((1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)*(1 - 3*x - x^2)*(1 - 3*x - 2*x^2)). - Colin Barker, Jul 17 2018
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EXAMPLE
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Some solutions for n=3:
..1.-2.-1..1...-1..1.-1.-1....1..1.-1.-2...-3..1..0..2....2..0..1..0
.-2..3..0..0....1.-1..1..1....1.-3..3..0....1..1.-2..0....0.-2..1.-2
.-1..0.-3..3...-1..1.-1.-1...-1..3.-3..0....0.-2..3.-1....1..1..0..1
..1..0..3.-3...-1..1.-1..3...-2..0..0..3....2..0.-1.-1....0.-2..1.-2
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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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