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%I #41 Dec 14 2023 05:32:35
%S 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,
%T -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
%N Expansion of (1 - 3x)/(1 - x + x^2).
%C Row sums of number triangle A117372.
%C Periodic sequence with period {1, -2, -3, -1, 2, 3}. - _Philippe Deléham_, Nov 03 2008
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1).
%F G.f.: (1 - 3x)/(1 - x + x^2).
%F a(n) = Sum_{k=0..n} (-1)^(n-k)*(C(k,n-k) + 3*C(k, n-k-1)).
%F a(n) = a(n-1) - a(n-2); a(0)=1, a(1)=-2. - _Philippe Deléham_, Nov 03 2008
%F a(n) = A010892(n) - 3*A010892(n-1). - _R. J. Mathar_, Sep 14 2013
%F a(n) = cos(n*Pi/3) - 5*sin(n*Pi/3)/sqrt(3). - _Andres Cicuttin_, Apr 06 2016
%F a(n) = ((n mod 3)^2 - 4*(n mod 3) + 1)*(-1)^floor(n/3). - _Luce ETIENNE_, Nov 18 2017
%t CoefficientList[Series[(1 - 3 x)/(1 - x + x^2), {x, 0, 200}], x] (* _Vladimir Joseph Stephan Orlovsky_, Jun 11 2011 *)
%o (PARI) Vec((1-3*x)/(1-x+x^2) + O(x^90)) \\ _Michel Marcus_, Apr 06 2016
%Y Cf. A010892, A117372.
%Y Cf. A010872 (n mod 3), A010875 (n mod 6).
%K easy,sign
%O 0,2
%A _Paul Barry_, Mar 10 2006
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