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URL: https://oeis.org/A257076

⇱ A257076 - OEIS

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A257076
Expansion of (1 - x^3) / (1 - x + x^2) in powers of x.
5
1, 1, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0
OFFSET
0,4
FORMULA
Euler transform of length 6 sequence [ 1, -1, -2, 0, 0, 1].
G.f.: (1 - x^2) * (1 - x^3)^2 / ((1 - x) * (1 - x^6)).
a(n) = -a(n+3) if n>1.
a(n) = A109265(n-1) if n>0.
Convolution inverse of A257075.
a(n) = A130772(n) for n>1. - R. J. Mathar, Apr 19 2015
a(n) = A184334(n+1) if n>1. - Michael Somos, Sep 01 2015
EXAMPLE
G.f. = 1 + x - 2*x^3 - 2*x^4 + 2*x^6 + 2*x^7 - 2*x^9 - 2*x^10 + 2*x^12 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1 - x^3) / (1 - x + x^2), {x, 0, n}];
Join[{1, 1}, LinearRecurrence[{1, -1}, {0, -2}, 76]] (* Ray Chandler, Aug 10 2015 *)
PROG
(PARI) {a(n) = n++; if( n<3, n>0, 2 * (n%3>0) * (-1)^(n\3))};
(PARI) {a(n) = if( n<0, 0, polcoeff( (1 - x^3) / (1 - x + x^2) + x * O(x^n), n))};
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 - x^3)/(1-x+x^2))); // G. C. Greubel, Aug 03 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Michael Somos, Apr 15 2015
STATUS
approved