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Search: id:A112300
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| A112300 |
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Expansion of x(1-x)^2(1-x^2)/(1-x^6) in powers of x. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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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.
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PROGRAM
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(PARI) a(n)=[0, 1, -2, 0, 2, -1][n%6+1]
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CROSSREFS
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Sequence in context: A069848 A118682 A083054 this_sequence A049239 A036580 A101674
Adjacent sequences: A112297 A112298 A112299 this_sequence A112301 A112302 A112303
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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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