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A078032 Expansion of (1-x)/(1+x^2+x^3). 1
1, -1, -1, 0, 2, 1, -2, -3, 1, 5, 2, -6, -7, 4, 13, 3, -17, -16, 14, 33, 2, -47, -35, 45, 82, -10, -127, -72, 137, 199, -65, -336, -134, 401, 470, -267, -871, -203, 1138, 1074, -935, -2212, -139, 3147, 2351, -3008, -5498, 657, 8506, 4841, -9163, -13347, 4322, 22510, 9025, -26832, -31535, 17807, 58367 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

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

FORMULA

a(0)=1, a(1)=-1, a(2)=-1, a(n) = -a(n-2) - a(n-3). - Harvey P. Dale, Sep 14 2012

MAPLE

seq(coeff(series((1-x)/(1+x^2+x^3), x, n+1), x, n), n = 0..60); # G. C. Greubel, Aug 05 2019

MATHEMATICA

CoefficientList[Series[(1-x)/(1+x^2+x^3), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, -1, -1}, {1, -1, -1}, 60] (* Harvey P. Dale, Sep 14 2012 *)

PROG

(PARI) my(x='x+O('x^60)); Vec((1-x)/(1+x^2+x^3)) \\ G. C. Greubel, Aug 05 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x)/(1+x^2+x^3) )); // G. C. Greubel, Aug 05 2019

(Sage) ((1-x)/(1+x^2+x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 05 2019

(GAP) a:=[1, -1, -1];; for n in [4..60] do a[n]:=-a[n-2]-a[n-3]; od; a; # G. C. Greubel, Aug 05 2019

CROSSREFS

Sequence in context: A101391 A327632 A117704 * A162453 A008313 A334550

Adjacent sequences:  A078029 A078030 A078031 * A078033 A078034 A078035

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified March 3 14:58 EST 2021. Contains 341762 sequences. (Running on oeis4.)