login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A163817 Expansion of (1 - x^2) * (1 - x^5) / ((1 - x) * (1 - x^6)) in powers of x. 3
1, 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
LINKS
FORMULA
Euler transform of length 6 sequence [ 1, -1, 0, 0, -1, 1].
a(n) is multiplicative with a(2^e) = a(3^e) = 0^e, a(p^e) = 1 if p == 1 (mod 6), a(p^e) = (-1)^e if p == 5 (mod 6).
a(2*n) = a(3*n) = 0 unless n=0, a(6*n + 5) = -1, a(6*n + 1) = a(0) = 1.
a(-n) = -a(n) unless n=0. a(n+6) = a(n) unless n=0 or n=-6.
G.f.: (1 + x + x^2 + x^3 + x^4) / (1 + x^2 + x^4).
a(n) = A134667(n), n>0. - R. J. Mathar, Aug 05 2009
G.f. A(x) = 1 + x / (1 + x^4 / (1 + x^2)) = 1 / (1 - x / (1 + x / (1 - x^3 / (1 + x^2 / (1 - x / (1 + x)))))) . - Michael Somos, Jan 03 2013
EXAMPLE
1 + x - x^5 + x^7 - x^11 + x^13 - x^17 + x^19 - x^23 + x^25 - x^29 + ...
MATHEMATICA
Join[{1}, LinearRecurrence[{0, -1, 0, -1}, {1, 0, 0, 0}, 50]] (* G. C. Greubel, Aug 04 2017 *)
PROG
(PARI) {a(n) = (n==0) + [0, 1, 0, 0, 0, -1][n%6 + 1]}
(PARI) {a(n) = (n==0) + kronecker(-12, n)}
CROSSREFS
A163811(n) = -a(n) unless n=0. A163811(n) = (-1)^n * a(n).
Convolution inverse of A163818.
Sequence in context: A185125 A327580 A163811 * A266837 A321081 A267126
KEYWORD
sign,easy,mult
AUTHOR
Michael Somos, Aug 04 2009
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 21 20:59 EDT 2024. Contains 374475 sequences. (Running on oeis4.)