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A211813
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Number of (n+1) X (n+1) -10..10 symmetric matrices with every 2 X 2 subblock having sum zero and two distinct values.
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1
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32, 44, 62, 92, 140, 218, 344, 548, 878, 1412, 2276, 3674, 5936, 9596, 15518, 25100, 40604, 65690, 106280, 171956, 278222, 450164, 728372, 1178522, 1906880, 3085388, 4992254, 8077628, 13069868, 21147482, 34217336, 55364804, 89582126, 144946916
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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) - a(n-3).
Empirical g.f.: 2*x*(16 - 10*x - 13*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 20 2018
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EXAMPLE
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Some solutions for n=3:
.-1..1.-1..1...-9..3.-3..3....3.-1..1.-3...-7..7.-7..7....1.-1.-1.-1
..1.-1..1.-1....3..3.-3..3...-1.-1..1..1....7.-7..7.-7...-1..1..1..1
.-1..1.-1..1...-3.-3..3.-3....1..1.-1.-1...-7..7.-7..7...-1..1.-3..1
..1.-1..1.-1....3..3.-3..3...-3..1.-1..3....7.-7..7.-7...-1..1..1..1
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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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