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A110161 Expansion of x(1-x^2)/(1-x^2+x^4). 12
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; text; internal format)
OFFSET
0,1
COMMENTS
Transform of A002605 by the Riordan array A102587. Denominator is the 12th cyclotomic polynomial.
LINKS
FORMULA
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
a(2*n - 1) = A010892(n). - Michael Somos, Jan 29 2015
a(n) = A014021(n+1). - R. J. Mathar, Nov 13 2023
MATHEMATICA
a[ n_] := JacobiSymbol[ 12, n]; (* Michael Somos, Jan 29 2015 *)
LinearRecurrence[{0, 1, 0, -1}, {0, 1, 0, 0}, 110] (* Harvey P. Dale, Jul 11 2015 *)
PROG
(PARI) {a(n) = kronecker( 12, n)}; /* Michael Somos, Jun 11 2007 */
CROSSREFS
Sequence in context: A317542 A322796 A109017 * A134667 A354354 A117943
KEYWORD
easy,sign,mult
AUTHOR
Paul Barry, Jul 14 2005
EXTENSIONS
Corrected by T. D. Noe, Dec 12 2006
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)