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A280166
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a(2*n) = 4*n if n>0, a(2*n + 1) = -(2*n + 1), a(0) = 1.
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1
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1, -1, 4, -3, 8, -5, 12, -7, 16, -9, 20, -11, 24, -13, 28, -15, 32, -17, 36, -19, 40, -21, 44, -23, 48, -25, 52, -27, 56, -29, 60, -31, 64, -33, 68, -35, 72, -37, 76, -39, 80, -41, 84, -43, 88, -45, 92, -47, 96, -49, 100, -51, 104, -53, 108, -55, 112, -57, 116
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OFFSET
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0,3
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LINKS
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FORMULA
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Euler transform of length 6 sequence [-1, 4, 1, -1, 0, -1].
G.f.: (1 - x + x^2) * (1 + x^2) / (1 - x^2)^2.
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EXAMPLE
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G.f. = 1 - x + 4*x^2 - 3*x^3 + 8*x^4 - 5*x^5 + 12*x^6 - 7*x^7 + 16*x^8 + ...
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MATHEMATICA
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a[ n_] := Which[ n < 1, Boole[n == 0], OddQ[n], -n, True, 2 n];
a[ n_] := SeriesCoefficient[ (1 - x + x^2) (1 + x^2) / (1 - x^2)^2, {x, 0, n}];
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PROG
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(PARI) {a(n) = if( n<1, n==0, n%2, -n, 2*n)};
(PARI) x='x+O('x^50); Vec((1-x+x^2)*(1+x^2)/(1-x^2)^2) \\ G. C. Greubel, Aug 04 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 - x+x^2)*(1+x^2)/(1-x^2)^2)); // G. C. Greubel, Aug 04 2018
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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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