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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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0
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Periodic with period length 8.
Sum_{k>=1} a(k)/k = Pi/8 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 20 2009]
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LINKS
| M. Somos, Rational Function Multiplicative Coefficients
Index to sequences with linear recurrences with constant coefficients, signature (0,-1,0,-1,0,-1).
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FORMULA
| 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 + x^2) * (1 - x)^2 /( (1 + x^2) * (1 + x^4)). a(n) = -a(4 - n) = a(n + 8). a(4*n) = 0.
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EXAMPLE
| x - x^2 - x^3 + x^5 + x^6 - x^7 + x^9 - x^10 - x^11 + x^13 + x^14 - x^15 + ...
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PROG
| (PARI) {a(n) = [ 0, 1, -1, -1, 0, 1, 1, -1][n%8 + 1]}
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CROSSREFS
| Sequence in context: A132350 A076213 A120525 * A014677 A175087 A127872
Adjacent sequences: A112296 A112297 A112298 * A112300 A112301 A112302
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KEYWORD
| sign,mult
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AUTHOR
| Michael Somos, Sep 02 2005
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