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A211324
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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 one or three distinct values.
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1
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15, 29, 55, 107, 209, 409, 805, 1583, 3127, 6175, 12233, 24241, 48141, 95655, 190343, 378967, 755249, 1505841, 3004341, 5996175, 11972503, 23911631, 47770041, 95451441, 190761021, 381287447, 762198439, 1523777639, 3046559585, 6091487857
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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) = 3*a(n-1) + 2*a(n-2) - 11*a(n-3) + a(n-4) + 12*a(n-5) - 2*a(n-6) - 4*a(n-7).
Empirical g.f.: x*(15 - 16*x - 62*x^2 + 49*x^3 + 82*x^4 - 36*x^5 - 36*x^6) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)). - Colin Barker, Jul 16 2018
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EXAMPLE
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Some solutions for n=3:
.-1..0.-1..0....2..0..2.-1....0..0..1..0....0..0..0.-1...-2..0.-2..1
..0..1..0..1....0.-2..0.-1....0..0.-1..0....0..0..0..1....0..2..0..1
.-1..0.-1..0....2..0..2.-1....1.-1..2.-1....0..0..0.-1...-2..0.-2..1
..0..1..0..1...-1.-1.-1..0....0..0.-1..0...-1..1.-1..2....1..1..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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