login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A163811
Expansion of (1 - x) * (1 - x^10) / ((1 - x^5) * (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
OFFSET
0,1
FORMULA
Euler transform of length 10 sequence [ -1, 0, 0, 0, 1, 1, 0, 0, 0, -1].
a(2*n) = a(3*n) = 0 unless n=0, a(6*n + 1) = -1, a(6*n + 5) = 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).
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
A163817(n) = -a(n) unless n=0. A163817(n) = (-1)^n * a(n).
Convolution inverse of A163812.
Sequence in context: A185124 A185125 A327580 * A163817 A266837 A321081
KEYWORD
sign,easy
AUTHOR
Michael Somos, Aug 04 2009, Aug 09 2009
STATUS
approved