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A211336
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Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values
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1
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60, 332, 1846, 10332, 58164, 329130, 1870664, 10670876, 61044918, 349974788, 2009495068, 11549465226, 66414142512, 381959562756, 2196335839046, 12624063953180, 72516570941316, 416247502883594, 2387248114517560
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OFFSET
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1,1
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COMMENTS
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Symmetry and 2X2 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) = 32*a(n-1) -429*a(n-2) +3078*a(n-3) -12340*a(n-4) +24890*a(n-5) -10895*a(n-6) -35870*a(n-7) +19131*a(n-8) +40338*a(n-9) +18694*a(n-10) +3532*a(n-11) +240*a(n-12)
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EXAMPLE
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Some solutions for n=3
.-3..1.-1..2....5.-3..0.-4....5.-2..4.-5....2..0.-1.-2....2.-1.-1..1
..1..1.-1..0...-3..1..2..2...-2.-1.-1..2....0.-2..3..0...-1..0..2.-2
.-1.-1..1..0....0..2.-5..1....4.-1..3.-4...-1..3.-4..1...-1..2.-4..4
..2..0..0.-1...-4..2..1..3...-5..2.-4..5...-2..0..1..2....1.-2..4.-4
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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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