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A092220
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Expansion of x(1-x)/(1+x^3).
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4
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0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Multiplicative with a(2^e) = -1, a(3^e) = 0, a(p^e) = 1 otherwise. David W. Wilson (davidwwilson(AT)comcast.net) Jun 12, 2005.
a(n)=3a(n-1)-a(n-3)+3a(n-4). - Paul Curtz (bpcrtz(AT)free.fr), Dec 10 2007
The BINOMIAL transform generates (-1)^(n+1)*A024495(n+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2008
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LINKS
| M. Somos, Rational Function Multiplicative Coefficients
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FORMULA
| Euler transform of length 6 sequence [ -1, 0, -1, 0, 0, 1]. - Michael Somos Apr 10 2011
Moebius transform is length 6 sequence [ 1, -2, -1, 0, 0, 2]. - Michael Somos Apr 10 2011
G.f.: x * (1 - x) * (1 - x^3) / (1 - x^6). a(n) = a(-n). a(n + 3) = -a(n). a(3*n) = 0. - Michael Somos Apr 10 2011
a(n)=2cos(pi*n/3)/3-2(-1)^n/3
Transform of the Jacobsthal numbers A001045 under the Riordan array A102587. - Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
a(n)=(1/6)*{(n mod 6)-2*[(n+1) mod 6]+[(n+2) mod 6]-[(n+3) mod 6]+2*[(n+4) mod 6]-[(n+5) mod 6]}, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Feb 05 2008
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EXAMPLE
| x - x^2 - x^4 + x^5 + x^7 - x^8 - x^10 + x^11 + x^13 - x^14 - x^16 + x^17 + ...
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PROG
| (PARI) {a(n) = [ 0, 1, -1, 0, -1, 1][n%6 + 1]} /* Michael Somos Apr 10 2011 */
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CROSSREFS
| Sequence in context: A082410 A094217 A174784 * A011655 A102283 A128834
Adjacent sequences: A092217 A092218 A092219 * A092221 A092222 A092223
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KEYWORD
| easy,sign,mult
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 25 2004
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