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A199697
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Number of -1..1 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.
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3
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1, 2, 6, 8, 14, 32, 56, 100, 204, 388, 722, 1416, 2750, 5256, 10222, 19944, 38650, 75272, 147142, 287120, 561018, 1098752, 2152092, 4217620, 8276376, 16250292, 31921374, 62754072, 123440514, 242921784, 478310952, 942260548, 1856994908, 3661288036
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: ((x+1)^2*sqrt((1-x)/(1-x-4*x^3))-2*x-1)/x. - Stefan Hollos, Mar 08 2017
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EXAMPLE
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All solutions for n=5
..0...-1....1...-1....1...-1...-1....0....1...-1....0....1....1....0
.-1....1...-1....1....0....1....0...-1...-1....1....1...-1...-1....1
..1....0....0...-1...-1...-1....1....0....1....0....0....1....0...-1
.-1...-1....1....1....1....0...-1....1....0....1...-1...-1...-1....1
..1....1...-1....0...-1....1....1....0...-1...-1....0....0....1...-1
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MATHEMATICA
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Rest@ CoefficientList[Series[((x + 1)^2*Sqrt[(1 - x)/(1 - x - 4*x^3)] - 2 x - 1)/x, {x, 0, 34}], x] (* Michael De Vlieger, Mar 08 2017 *)
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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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