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A078029 Expansion of (1-x)/(1-2*x^3). 1
1, -1, 0, 2, -2, 0, 4, -4, 0, 8, -8, 0, 16, -16, 0, 32, -32, 0, 64, -64, 0, 128, -128, 0, 256, -256, 0, 512, -512, 0, 1024, -1024, 0, 2048, -2048, 0, 4096, -4096, 0, 8192, -8192, 0, 16384, -16384, 0, 32768, -32768, 0, 65536, -65536, 0, 131072, -131072, 0, 262144, -262144, 0, 524288, -524288, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,2).

FORMULA

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

a(n) = (-1)^floor(4n/3)*(2-2*0^mod(n+1,3))^floor((n+1)/3). - Wesley Ivan Hurt, May 09 2015

a(n) = A077958(n) - A077958(n-1). - R. J. Mathar, Mar 04 2018

MAPLE

seq(op([2^n, -2^n, 0]), n=0..60); # Robert Israel, May 11 2015

MATHEMATICA

CoefficientList[Series[(1-x)/(1-2*x^3), {x, 0, 60}], x] (* Vincenzo Librandi, May 10 2015 *)

PROG

(MAGMA) &cat[[2^n, -2^n, 0]: n in [0..60]]; // Vincenzo Librandi, May 10 2015

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

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

(GAP) a:=[1, -1, 0];; for n in [4..60] do a[n]:=2*a[n-3]; od; a; # G. C. Greubel, Aug 05 2019

CROSSREFS

Sequence in context: A141333 A262967 A168090 * A078030 A262056 A264628

Adjacent sequences:  A078026 A078027 A078028 * A078030 A078031 A078032

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified April 21 19:16 EDT 2021. Contains 343156 sequences. (Running on oeis4.)