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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
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

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Last modified July 23 21:46 EDT 2024. Contains 374575 sequences. (Running on oeis4.)