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A211329
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Number of (n+1) X (n+1) -5..5 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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15, 19, 25, 35, 51, 77, 119, 187, 297, 475, 763, 1229, 1983, 3203, 5177, 8371, 13539, 21901, 35431, 57323, 92745, 150059, 242795, 392845, 635631, 1028467, 1664089, 2692547, 4356627, 7049165, 11405783, 18454939, 29860713, 48315643, 78176347
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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*(15 - 11*x - 13*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 17 2018
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EXAMPLE
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Some solutions for n=3:
.-1..1.-1.-1....4.-4..4.-4....1..1..1.-1....1.-1..1..1...-2..2.-2..2
..1.-1..1..1...-4..4.-4..4....1.-3..1.-1...-1..1.-1.-1....2.-2..2.-2
.-1..1.-1.-1....4.-4..4.-4....1..1..1.-1....1.-1..1..1...-2..2.-2..2
.-1..1.-1..3...-4..4.-4..4...-1.-1.-1..1....1.-1..1.-3....2.-2..2.-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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