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 A100219 Expansion of (1-2*x)/((1-x)*(1-x+x^2)). 7
 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 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: A343230 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 19 12:12 EDT 2021. Contains 345128 sequences. (Running on oeis4.)