This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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