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A117373 Expansion of (1 - 3x)/(1 - x + x^2). 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Row sums of number triangle A117372.
Periodic sequence with period {1, -2, -3, -1, 2, 3}. - Philippe Deléham, Nov 03 2008
LINKS
Tanya Khovanova, Recursive Sequences
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) = A010892(n) - 3*A010892(n-1). - R. J. Mathar, Sep 14 2013
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
MATHEMATICA
CoefficientList[Series[(1 - 3 x)/(1 - x + x^2), {x, 0, 200}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
PROG
(PARI) Vec((1-3*x)/(1-x+x^2) + O(x^90)) \\ Michel Marcus, Apr 06 2016
CROSSREFS
Cf. A010872 (n mod 3), A010875 (n mod 6).
Sequence in context: A294180 A179542 A082846 * A132677 A010882 A343638
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 10 2006
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)