OFFSET
0,1
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..999
Michael Somos, Rational Function Multiplicative Coefficients
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).
FORMULA
Euler transform of length 9 sequence [1, 0, 0, 0, 0, 0, 0, -1, 1]. - Michael Somos, Mar 22 2011
Moebius transform is length 9 sequence [1, 0, 0, 0, 0, 0, 0, 0, -1]. - Michael Somos, Mar 22 2011
Expansion of x * (1 - x^8) / ((1 - x) * (1 - x^9)) in powers of x. - Michael Somos, Mar 22 2011
Multiplicative with a(p^e) = (if p=3 then 0^(e-1) else 1), p prime and e>0.
a(n) = a(n+9) = a(-n) for all n in Z.
A033441(n) = Sum_{k=0..n} a(k)*(n-k).
G.f.: -x*(1+x)*(1+x^2)*(1+x^4) / ( (x-1)*(1+x+x^2)*(x^6+x^3+1) ). - R. J. Mathar, Jan 07 2011
Dirichlet g.f. (1-3^(-2s))*zeta(s). - R. J. Mathar, Mar 06 2011
For the general case: the characteristic function of numbers that are not multiples of m is a(n)=floor((n-1)/m)-floor(n/m)+1, m,n > 0. - Boris Putievskiy, May 08 2013
a(n) = 1 - A267142(n). - Antti Karttunen, Oct 07 2017
EXAMPLE
G.f. = x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^10 + x^11 + x^12 + x^13 + ...
PROG
(PARI) {a(n) = sign(n%9)}; /* Michael Somos, Mar 22 2011 */
CROSSREFS
KEYWORD
easy,mult,nonn
AUTHOR
Reinhard Zumkeller, Nov 30 2009
STATUS
approved