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A168361
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Period 2: repeat 2, -1.
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6
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2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1
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OFFSET
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1,1
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COMMENTS
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Binomial transform of 2 followed by a signed version of A007283; also binomial transform of a signed version of A042950.
Second binomial transform of a signed version of A007051 without initial term 1.
Inverse binomial transform of 2 followed by A000079.
A028242 without first two terms gives partial sums.
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LINKS
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FORMULA
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a(n) = (1 - 3*(-1)^n)/2.
a(n) = -a(n-1) + 1 for n > 1; a(1) = 2.
a(n) = a(n-2) for n > 2; a(1) = 2, a(2) = -1.
a(n+1) - a(n) = 3*(-1)^n.
G.f.: x*(2 - x)/((1-x)*(1+x)).
E.g.f.: (1/2)*(-1 + exp(x))*(3 + exp(x))*exp(-x). - G. C. Greubel, Jul 19 2016
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MATHEMATICA
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Table[(1 - 3 (-1)^n)/2, {n, 120}] (* or *)
Rest@ CoefficientList[Series[x (2 - x)/((1 - x) (1 + x)), {x, 0, 120}], x] (* Michael De Vlieger, Jul 19 2016 *)
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PROG
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(Magma) &cat[ [2, -1]: n in [1..42] ];
[ n eq 1 select 2 else -Self(n-1)+1: n in [1..84] ];
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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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