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A211253
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Number of (n+1) X (n+1) -6..6 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
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1
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21, 29, 41, 61, 93, 145, 229, 365, 585, 941, 1517, 2449, 3957, 6397, 10345, 16733, 27069, 43793, 70853, 114637, 185481, 300109, 485581, 785681, 1271253, 2056925, 3328169, 5385085, 8713245, 14098321, 22811557, 36909869, 59721417, 96631277
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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.: x*(21 - 13*x - 17*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 16 2018
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EXAMPLE
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Some solutions for n=3:
.-1.-1.-1.-1...-3..1.-1..3....3.-1..1.-3....2.-2..2..2...-1..1..1..1
.-1..3.-1..3....1..1.-1.-1...-1.-1..1..1...-2..2.-2.-2....1.-1.-1.-1
.-1.-1.-1.-1...-1.-1..1..1....1..1.-1.-1....2.-2..2..2....1.-1..3.-1
.-1..3.-1..3....3.-1..1.-3...-3..1.-1..3....2.-2..2.-6....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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