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A100219 Expansion of (1-2*x)/((1-x)*(1-x+x^2)). 2
1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0, 1, 0, -2, -3, -2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums of number triangle A100218.

LINKS

Table of n, a(n) for n=0..71.

Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

FORMULA

a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3).

a(n) = cos(Pi*n/3 + Pi/3) + sqrt(3)*sin(Pi*n/3 + Pi/3) - 1.

MATHEMATICA

CoefficientList[Series[(1 - 2*x)/((1 - x)*(1 - x + x^2)), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -2, 1}, {1, 0, -2}, 50] (* G. C. Greubel, Mar 13 2017 *)

Table[Cos[Pi*n/3 + Pi/3] + Sqrt[3]*Sin[Pi*n/3 + Pi/3] - 1, {n, 0, 71}] (* Indranil Ghosh, Mar 13 2017 *)

PROG

(PARI) x='x+O('x^50); Vec((1-2*x)/((1-x)*(1-x+x^2))) \\ G. C. Greubel, Mar 13 2017

CROSSREFS

Cf. A079757.

Sequence in context: A027413 A019509 A071484 * A079757 A071493 A289813

Adjacent sequences:  A100216 A100217 A100218 * A100220 A100221 A100222

KEYWORD

easy,sign

AUTHOR

Paul Barry, Nov 08 2004

STATUS

approved

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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)