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A110161 Expansion of x(1-x^2)/(1-x^2+x^4). 7
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

Table of n, a(n) for n=0..104.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1).

FORMULA

Periodic of length 12: 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1. - T. D. Noe, 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, 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) for all n in Z. - Michael Somos, Jun 11 2007

a(2*n - 1) = A010892(n). - Michael Somos, Jan 29 2015

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

Cf. A010892.

Sequence in context: A317542 A322796 A109017 * A134667 A117943 A285969

Adjacent sequences:  A110158 A110159 A110160 * A110162 A110163 A110164

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 July 21 00:49 EDT 2019. Contains 325189 sequences. (Running on oeis4.)