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PadRight[{}, 120, {1, -2, 0, 2, -1, 0}] (* Harvey P. Dale, Jul 09 2019 *)

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Expansion of x( * (1- - x)^2( * (1- - x^2)/() / (1- - x^6) in powers of x.

Multiplicative with a(2^e) = 2(-*(-1)^e if e>0, a(3^e) = 0 if e>0, a(p^e) = 1 if p == 1 (mod 6), a(p^e) = (-1)^e if p == 5 (mod 6).

G.f.: x( * (1- - x)^2( / ((1- - x + x^2)/() * (1- + x + x^6). a(n)=-a(3-n)=a(n+6). a(3n)=0.2)). - _Michael Somos_, May 04 2015

G.f.: -(f(x) + 3*f(-x)) / 2 where f(x) := x / (1 - x + x^2). - Michael Somos, May 04 2015

a(n) = -a(3 - n) = a(n+6), a(3*n) = 0 for all n in Z.

G.f. = x - 2*x^2 + 2*x^4 - x^5 + x^7 - 2*x^8 + 2*x^10 - x^11 + x^13 - 2*x^14 + ...

a[ n_] := {0, 1, -2, 0, 2, -1} [[ Mod[n, 6] + 1]]; (* Michael Somos, May 04 2015 *)

(PARI) ) {a(n)=[) = [0, , 1, -, -2, , 0, , 2, -, -1][n%6+ + 1]]};

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Michael Somos: Added more info. Light and space edits.

_Michael Somos, _, Sep 02 2005

OEIS Server: https://oeis.org/edit/global/2183

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sign,easy,mult

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Euler transform of length 6 sequence [ -2,-, -1,, 0,, 0,, 0,, 1].

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Expansion of x(1-x)^2(1-x^2)/(1-x^6) in powers of x.

1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, -2, 0

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Euler transform of length 6 sequence [ -2,-1,0,0,0,1].

Multiplicative with a(2^e) = 2(-1)^e if e>0, a(3^e) = 0 if e>0, a(p^e) = 1 if p == 1 (mod 6), a(p^e) = (-1)^e if p == 5 (mod 6).

G.f.: x(1-x)^2(1-x^2)/(1-x^6). a(n)=-a(3-n)=a(n+6). a(3n)=0.

(PARI) a(n)=[0, 1, -2, 0, 2, -1][n%6+1]

sign,mult

Michael Somos, Sep 02 2005

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