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A163804 Expansion of (1 - x) * (1 - x^4) / ((1 - x^2) * (1 - x^3)) in powers of x. 3
1, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1, -1).

FORMULA

Euler transform of length 4 sequence [ -1, 1, 1, -1].

G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = 2 - v - u * (4 - 2*v - u).

a(3*n) = 0 unless n=0, a(3*n + 1) = -1, a(3*n + 2) = a(0) = 1.

a(-n) = -a(n) unless n=0. a(n+3) = a(n) unless n=0 or n=-3.

G.f.: (1 + x^2) / (1 + x + x^2).

G.f. A(x) = 1 / (1 + x / (1 + x^2)) = 1 - x / (1 + x / (1 - x / (1 + x))). - Michael Somos, Jan 03 2013

a(n) = A057078(n-2), n>1. - R. J. Mathar, Aug 06 2009

EXAMPLE

1 - x + x^2 - x^4 + x^5 - x^7 + x^8 - x^10 + x^11 - x^13 + x^14 + ...

MATHEMATICA

Join[{1}, LinearRecurrence[{-1, -1}, {-1, 1}, 105]] (* Ray Chandler, Sep 15 2015 *)

PROG

(PARI) {a(n) = (n==0) + [0, -1, 1][n%3 + 1]}

(PARI) {a(n) = (n==0) - kronecker(-3, n)}

CROSSREFS

A106510(n) = -a(n) unless n=0. Convolution inverse of A117659.

Sequence in context: A106510 A163806 A163810 * A181653 A155091 A145362

Adjacent sequences:  A163801 A163802 A163803 * A163805 A163806 A163807

KEYWORD

sign,easy

AUTHOR

Michael Somos, Aug 04 2009

STATUS

approved

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Last modified July 22 17:02 EDT 2019. Contains 325225 sequences. (Running on oeis4.)