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A211333
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Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values
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1
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61, 153, 359, 811, 1825, 4073, 9117, 20435, 46019, 104103, 236721, 541185, 1243505, 2872291, 6664963, 15538035, 36366709, 85451073, 201438293, 476368999, 1129466571, 2684618219, 6394000481, 15257754137, 36465654269, 87277538267
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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) = 5*a(n-1) +10*a(n-2) -82*a(n-3) -10*a(n-4) +576*a(n-5) -286*a(n-6) -2266*a(n-7) +1807*a(n-8) +5476*a(n-9) -5310*a(n-10) -8379*a(n-11) +9038*a(n-12) +8059*a(n-13) -9334*a(n-14) -4671*a(n-15) +5778*a(n-16) +1496*a(n-17) -2024*a(n-18) -226*a(n-19) +356*a(n-20) +12*a(n-21) -24*a(n-22)
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EXAMPLE
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Some solutions for n=3
..0..1..0..0....0..2..1..2....2..1..2..1...-2..1..1..1...-3..1.-3..1
..1.-2..1.-1....2.-4..1.-4....1.-4..1.-4....1..0.-2..0....1..1..1..1
..0..1..0..0....1..1..2..1....2..1..2..1....1.-2..4.-2...-3..1.-3..1
..0.-1..0..0....2.-4..1.-4....1.-4..1.-4....1..0.-2..0....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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