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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

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

Index entries for linear recurrences with constant coefficients, signature (0, -1, 0, -1).

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: A185124 A185125 A163811 * A151667 A015274 A011651

Adjacent sequences:  A163814 A163815 A163816 * A163818 A163819 A163820

KEYWORD

sign,easy,mult

AUTHOR

Michael Somos, Aug 04 2009

STATUS

approved

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Last modified February 24 13:14 EST 2018. Contains 299623 sequences. (Running on oeis4.)