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A211476
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Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having one or three distinct values for every i<=n and j<=n.
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1
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7, 17, 37, 79, 165, 339, 693, 1403, 2837, 5707, 11477, 23019, 46165, 92459, 185173, 370603, 741717, 1483947, 2968917, 5938859, 11879765, 23761579, 47527253, 95058603, 190125397, 380258987, 760534357, 1521085099, 3042202965, 6084438699
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = a(n-1) + 4*a(n-2) - 2*a(n-3) - 4*a(n-4).
G.f.: x*(7 + 10*x - 8*x^2 - 12*x^3) / ((1 + x)*(1 - 2*x)*(1 - 2*x^2)).
a(n) = (-9*2^(n/2) + 17*2^n + 1)/3 for n even.
a(n) = (17*2^n - 3*2^((n+3)/2) - 1)/3 for n odd.
(End)
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EXAMPLE
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Some solutions for n=5:
..0....0....0...-1....0....1....1....0....0....1....0....0....1...-1....0....1
..0....1....0....1....0...-1....0...-1....1...-1....1....0....0....0....1....0
.-1....0...-1....0....0....1....0....0...-1....0...-1....0...-1....0....0....0
..0....0....0...-1...-1...-1....0...-1....0...-1....1....1....0....1...-1....0
..1....0....0....0....0....1...-1....0....1....1....0....0...-1....0....1....1
..0...-1....1...-1...-1....0....0....0...-1...-1....1....1....1....1....0....0
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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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