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A100047
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A Chebyshev transform of the Fibonacci numbers.
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5
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0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Multiplicative with a(p^e) = -1^(e+1) if p = 2, 0 if p = 5, 1 if p == 1 or 9 (mod 10), -1^e if p == 3 or 7 (mod 10). David W. Wilson (davidwwilson(AT)comcast.net) Jun 10, 2005.
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FORMULA
| G.f.: x(1-x^2)/(1-x+x^2-x^3+x^4); a(n)=a(n-1)-a(n-2)+a(n-3)-a(n-4); a(n)=n*sum{k=0..floor(n/2), (-1)^k*binomial(n-k, k)A000045(n-2k)/(n-k)}.
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EXAMPLE
| A Chebyshev transform of the Fibonacci numbers A000045: if A(x) is the
g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
The denominator is the 10th cyclotomic polynomial.
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CROSSREFS
| Cf. A099443, A011655, A100048.
Sequence in context: A092248 A106743 A011558 * A080891 A112713 A143536
Adjacent sequences: A100044 A100045 A100046 * A100048 A100049 A100050
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KEYWORD
| easy,sign,mult
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 31 2004
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