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A105384
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Expansion of x/(1 + x + x^2 + x^3 + x^4).
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3
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0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0
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OFFSET
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0,1
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COMMENTS
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Inverse binomial transform of A103311. A transform of the Fibonacci numbers: apply the Chebyshev transform (1/(1+x^2), x/(1+x^2)) followed by the binomial involution (1/(1-x),-x/(1-x)) followed by the inverse binomial transform (1/(1+x), x/(1+x)) (expressed as Riordan arrays) to the -F(n); equivalently, apply (1/(1+x^2),-x/(1+x^2)) to -F(n). Periodic {0,1,-1,0,0}.
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LINKS
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FORMULA
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Euler transform of length 5 sequence [ -1, 0, 0, 0, 1].
G.f.: x(1-x)/(1-x^5);
a(n) = -sqrt(1/5 + 2*sqrt(5)/25)*cos(4*Pi*n/5 + Pi/10) + sqrt(5)*sin(4*Pi*n/5 + Pi/10)/5 + sqrt(1/5 - 2*sqrt(5)/25)*cos(2*Pi*n/5 + 3*Pi/10) + sqrt(5)*sin(2*Pi*n/5 + 3*Pi/10)/5.
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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