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A110161
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Expansion of x(1-x^2)/(1-x^2+x^4).
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12
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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
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OFFSET
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0,1
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COMMENTS
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Transform of A002605 by the Riordan array A102587. Denominator is the 12th cyclotomic polynomial.
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LINKS
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FORMULA
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Periodic of length 12: 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1. - T. D. Noe, Dec 12 2006
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) for all n in Z. - Michael Somos, Jun 11 2007
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MATHEMATICA
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LinearRecurrence[{0, 1, 0, -1}, {0, 1, 0, 0}, 110] (* Harvey P. Dale, Jul 11 2015 *)
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PROG
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(PARI) {a(n) = kronecker( 12, n)}; /* Michael Somos, Jun 11 2007 */
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CROSSREFS
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KEYWORD
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easy,sign,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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