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Search: id:A112299
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| A112299 |
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Expansion of x(1-x)(1-x^2)(1-x^3)/(1-x^8) in powers of x. |
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1
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| 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 1
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Euler transform of length 8 sequence [ -1, -1, -1, 0, 0, 0, 0, 1].
Multiplicative with a(2) = -1, a(2^e) = 0 if e>1, a(p^e) = 1 if p == 1 (mod 4), a(p^e) = (-1)^e if p == 3 (mod 4).
G.f.: x(1-x)(1-x^2)(1-x^3)/(1-x^8). a(n)=-a(4-n)=a(n+8). a(4n)=0.
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PROGRAM
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(PARI) a(n)=[0, 1, -1, -1, 0, 1, 1, -1][n%8+1]
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CROSSREFS
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Adjacent sequences: A112296 A112297 A112298 this_sequence A112300 A112301 A112302
Sequence in context: A060038 A132350 A120525 this_sequence A071033 A014677 A127872
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Sep 02 2005
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