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A110161
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Expansion of x(1-x^2)/(1-x^2+x^4).
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1
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0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Transform of A002605 by the Riordan array A102587. Denominator is the 12th cyclotomic polynomial.
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FORMULA
| Periodic of length 12: 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1 - T. D. Noe (noe(AT)sspectra.com), Dec 12 2006
a(n)=(1/12)*{[n mod 12]-[(n+1) mod 12]-[(n+4) mod 12]+[(n+5) mod 12]-[(n+6) mod 12]+[(n+7) mod 12]+[(n+10) mod 12]-[(n+11) mod 12]}, with n>=0. - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 01 2007
Euler transform of length 12 sequence [ 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1]. - Michael Somos Jun 11 2007
a(n) is multiplicative with a(2^e) = a(3^e) = 0^e, a(p^e) = 1 if p == 1, 11 (mod 12), a(p^e) = (-1)^e if p == 5, 7 (mod 12). - Michael Somos Jun 11 2007
G.f.: x *(1-x^4) *(1-x^6)/ (1-x^12). a(n) = a(-n) = -a(n+6). - Michael Somos Jun 11 2007
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PROG
| (PARI) {a(n)= kronecker(12, n)} /* Michael Somos Jun 11 2007 */
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CROSSREFS
| Sequence in context: A122415 A109017 * A134667 A117943 A096268 A079101
Adjacent sequences: A110158 A110159 A110160 * A110162 A110163 A110164
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KEYWORD
| easy,sign,mult
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Dec 12 2006
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