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A101675 Expansion of (1-x-x^2)/(1+x^2+x^4). 3
1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums are A101676.

Periodic with period 6. - Ray Chandler, Sep 03 2015

LINKS

Table of n, a(n) for n=0..104.

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

FORMULA

a(0) = 1, a(1) = -1, a(2) = -2, a(3) = 1; for n >= 4, a(n)=-a(n-2)-a(n-4).

a(n) = sum{k=0..floor(n/2), (-1)^A010060(n-2k)*mod(binomial(n-k, k), 2)(-1)^k};

a(n) = cos(2*Pi*n/3+Pi/6)/sqrt(3)+sin(2*Pi*n/3+Pi/6)+cos(Pi*n/3+Pi/3)-sin(Pi*n/3+Pi/3)/sqrt(3).

MATHEMATICA

LinearRecurrence[{0, -1, 0, -1}, {1, -1, -2, 1}, 105] (* Ray Chandler, Sep 03 2015 *)

CoefficientList[Series[(1 - x - x^2)/(1 + x^2 + x^4), {x, 0, 150}], x] (* Vincenzo Librandi, Sep 04 2015 *)

PROG

(PARI) Vec((1-x-x^2)/(1+x^2+x^4) + O(x^80)) \\ Michel Marcus, Sep 04 2015

(MAGMA) I:=[1, -1, -2, 1]; [n le 4 select I[n] else -Self(n-2)-Self(n-4): n in [1..120]]; // Vincenzo Librandi, Sep 04 2015

CROSSREFS

Cf. A101676.

Sequence in context: A120936 A214438 A173432 * A051764 A268533 A275849

Adjacent sequences:  A101672 A101673 A101674 * A101676 A101677 A101678

KEYWORD

easy,sign

AUTHOR

Paul Barry, Dec 11 2004

STATUS

approved

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Last modified May 24 11:40 EDT 2017. Contains 286975 sequences.