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A134967
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List of quadruples: [-2n-1, 2n+2, -2n-1, 2n+2].
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6
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-1, 2, -1, 2, -3, 4, -3, 4, -5, 6, -5, 6, -7, 8, -7, 8, -9, 10, -9, 10, -11, 12, -11, 12, -13, 14, -13, 14, -15, 16, -15, 16, -17, 18, -17, 18, -19, 20, -19, 20, -21, 22, -21, 22, -23, 24, -23, 24, -25, 26, -25, 26, -27, 28, -27, 28, -29, 30, -29, 30, -31, 32, -31, 32, -33, 34, -33, 34, -35, 36, -35, 36, -37, 38, -37, 38, -39
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OFFSET
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0,2
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COMMENTS
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First differences are 3, -3, 3, -5, 7, -7, 7, -9, 11, -11, 11, ... .
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LINKS
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FORMULA
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a(n) = (1-(2*n+3)*(-1)^n-2*(-1)^((2*n+1-(-1)^n)/4))/4. - Luce ETIENNE, Sep 04 2016
a(n) = cos((n-1)*Pi)*(2*n+3+2*cos(n*Pi/2)-cos(n*Pi)+2*sin(n*Pi/2))/4. - Wesley Ivan Hurt, Oct 02 2017
G.f.: -(1 - x - x^2 - x^3) / ((1 - x)*(1 + x)^2*(1 + x^2)).
a(n) = (1 - 3*(-1)^n - (1-i)*(-i)^n - (1+i)*i^n - 2*(-1)^n*n) / 4 were i=sqrt(-1).
(End)
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MATHEMATICA
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Flatten[Table[{-2n-1, 2n+2, -2n-1, 2n+2}, {n, 0, 20}]] (* Harvey P. Dale, Oct 19 2011 *)
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PROG
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(Magma) [(1-(2*n+3)*(-1)^n-2*(-1)^((2*n+1-(-1)^n)div 4))/4: n in [0..80]]; /* or * / &cat [[-2*n-1, 2*n+2, -2*n-1, 2*n+2]: n in [0..30]]; // Vincenzo Librandi, Oct 04 2017
(PARI) Vec(-(1 - x - x^2 - x^3) / ((1 - x)*(1 + x)^2*(1 + x^2)) + O(x^100)) \\ Colin Barker, Oct 05 2017
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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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STATUS
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approved
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