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A134668
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Period 6: repeat [1, -1, 0, 0, -1, 1].
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2
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1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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Euler transform of length 6 sequence [-1, 0, 0, -1, 0, 1]. - Michael Somos, Feb 08 2008
G.f.: (1-x)*(1-x^4) / (1-x^6) = (1-x)*(1+x^2) / ((1-x+x^2)*(1+x+x^2)) = (1-x+x^2-x^3) / (1+x^2+x^4).
a(n) + a(n-2) + a(n-4) = 0 for n>3.
a(n) = cos(n*Pi/6) * (3*cos(n*Pi/2) + 2*sqrt(3)*sin(n*Pi/6) - 3*sqrt(3)*sin(n*Pi/2))/3. (End)
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EXAMPLE
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G.f. = 1 - x - x^4 + x^5 + x^6 - x^7 - x^10 + x^11 + x^12 - x^13 - x^16 + ...
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MAPLE
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MATHEMATICA
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PadRight[{}, 120, {1, -1, 0, 0, -1, 1}] (* or *) LinearRecurrence[{0, -1, 0, -1}, {1, -1, 0, 0}, 120] (* Harvey P. Dale, Dec 03 2012 *)
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PROG
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(PARI) {a(n)=[1, -1, 0, 0, -1, 1][n%6+1]}; /* Michael Somos, Feb 08 2008 */
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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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