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A112690 Expansion of 1/(1+x^2-x^3-x^5). 1
0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Partial sums are A112689.

LINKS

Table of n, a(n) for n=0..99.

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

FORMULA

G.f.: 1/((1+x^2)(1-x^3)).

a(n) = sum{k=0..n, sum{j=0..floor((k+1)/2)), (-1)^(k-j)*C(k-j+1, j-1)}}.

a(n+12) = a(n) = 1/6 + A057077(n+1)/2 + A061347(n+1)/3. [R. J. Mathar, Feb 23 2009]

a(n+10) = (A000100(n)(mod 2))*(-1)^(1+[n/2]). - John M. Campbell, Jul 07 2016

From Ilya Gutkovskiy, Jul 07 2016: (Start)

E.g.f.: (3*sin(x) + 3*cos(x) + exp(x) - 4*exp(-x/2)*cos(sqrt(3)*x/2))/6.

a(n) = (3*sin(Pi*n/2) + 3*cos(Pi*n/2) - 4*cos(2*Pi*n/3) + 1)/6. (End)

MATHEMATICA

LinearRecurrence[{0, -1, 1, 0, 1}, {0, 1, 0, -1, 1}, 100] (* Vincenzo Librandi, Jul 07 2016 *)

PROG

(PARI) concat(0, Vec(1/(1+x^2-x^3-x^5) + O(x^80))) \\ Michel Marcus, Jul 07 2016

(PARI) a(n) = round(real((exp(-2/3*I*n*Pi)*(-4+(3+3*I)*exp((I*n*Pi)/6) + 2*exp((2*I*n*Pi)/3) + (3-3*I)*exp((7*I*n*Pi)/6) - 4*exp((4*I*n*Pi)/3)))/12)) \\ Colin Barker, Jul 07 2016

CROSSREFS

Cf. A000100, A057077, A061347, A112689.

Sequence in context: A030308 A280237 A259044 * A115971 A072165 A072608

Adjacent sequences:  A112687 A112688 A112689 * A112691 A112692 A112693

KEYWORD

easy,sign

AUTHOR

Paul Barry, Sep 15 2005

STATUS

approved

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Last modified October 17 19:36 EDT 2018. Contains 316293 sequences. (Running on oeis4.)