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A211114
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Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values.
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1
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9, 19, 39, 81, 167, 341, 695, 1405, 2839, 5709, 11479, 23021, 46167, 92461, 185175, 370605, 741719, 1483949, 2968919, 5938861, 11879767, 23761581, 47527255, 95058605, 190125399, 380258989, 760534359, 1521085101, 3042202967, 6084438701
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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) = 2*a(n-1) + 3*a(n-2) - 6*a(n-3) - 2*a(n-4) + 4*a(n-5).
Empirical g.f.: x*(9 + x - 26*x^2 + 20*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 2*x^2)). - Colin Barker, Jul 15 2018
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EXAMPLE
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Some solutions for n=3:
..2.-1..1.-1....2..0..1.-2....2.-1..0.-1....0..1..1..0...-2..1.-2..1
.-1..0..0..0....0.-2..1..0...-1..0..1..0....1.-2..0.-1....1..0..1..0
..1..0..0..0....1..1..0.-1....0..1.-2..1....1..0..2.-1...-2..1.-2..1
.-1..0..0..0...-2..0.-1..2...-1..0..1..0....0.-1.-1..0....1..0..1..0
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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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