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A195084
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a(2n-1) = 2-n, a(2n) = 2+n.
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1
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1, 3, 0, 4, -1, 5, -2, 6, -3, 7, -4, 8, -5, 9, -6, 10, -7, 11, -8, 12, -9, 13, -10, 14, -11, 15, -12, 16, -13, 17, -14, 18, -15, 19, -16, 20, -17, 21, -18, 22, -19, 23, -20, 24, -21, 25, -22, 26, -23, 27, -24, 28, -25, 29, -26, 30, -27, 31, -28, 32, -29, 33
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OFFSET
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1,2
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COMMENTS
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Start with first term = 1, add 2, subtract 3, add 4, subtract 5 and so on.
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LINKS
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FORMULA
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G.f.: x*(1+4*x+2*x^2)/((1-x)*(1+x)^2).
a(n) = a(-n-1) = -((2*n+1)*a(n-1)-7*n)/(2*n-1) = -a(n-1)+a(n-2)+a(n-3).
a(n) = ((2*n+1)*(-1)^n+7)/4.
Sum(n=1..n, a(i)) = ((n+1)*(-1)^n+7*n-1)/4, i.e. A016777 and A008586 (>0) alternately. (End)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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