A117373 Expansion of (1 - 3x)/(1 - x + x^2).
1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1
Offset: 0
Links
- Tanya Khovanova, Recursive Sequences
- Index entries for linear recurrences with constant coefficients, signature (1,-1).
Programs
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Mathematica
CoefficientList[Series[(1 - 3 x)/(1 - x + x^2), {x, 0, 200}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *) -
PARI
Vec((1-3*x)/(1-x+x^2) + O(x^90)) \\ Michel Marcus, Apr 06 2016
Formula
G.f.: (1 - 3x)/(1 - x + x^2).
a(n) = Sum_{k=0..n} (-1)^(n-k)*(C(k,n-k) + 3*C(k, n-k-1)).
a(n) = a(n-1) - a(n-2); a(0)=1, a(1)=-2. - Philippe Deléham, Nov 03 2008
a(n) = cos(n*Pi/3) - 5*sin(n*Pi/3)/sqrt(3). - Andres Cicuttin, Apr 06 2016
a(n) = ((n mod 3)^2 - 4*(n mod 3) + 1)*(-1)^floor(n/3). - Luce ETIENNE, Nov 18 2017
Comments