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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 Index entries for linear recurrences with constant coefficients, signature (1,-1). 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) = (1/6)*(2*(n mod 6) - ((n+1) mod 6) - 3*((n+2) mod 6) - 2*((n+3) mod 6) + ((n+4) mod 6) + 3*((n+5) mod 6)), with n >= 1. - Paolo P. Lava, Apr 27 2007 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. A010892, A117372. Cf. A010872 (n mod 3), A010875 (n mod 6). Sequence in context: A294180 A179542 A082846 * A132677 A010882 A293207 Adjacent sequences:  A117370 A117371 A117372 * A117374 A117375 A117376 KEYWORD easy,sign AUTHOR Paul Barry, Mar 10 2006 STATUS approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)