Search: id:A101675
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%I A101675
%S A101675 1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,
%T A101675 0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,
%U A101675 1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,2
%V A101675 1,-1,-2,1,1,0,1,-1,-2,1,1,0,1,-1,-2,1,1,0,1,-1,-2,1,1,0,1,-1,-2,1,1,0,
               1,-1,-2,1,1,
%W A101675 0,1,-1,-2,1,1,0,1,-1,-2,1,1,0,1,-1,-2,1,1,0,1,-1,-2,1,1,0,1,-1,-2,1,1,
               0,1,-1,-2,1,
%X A101675 1,0,1,-1,-2,1,1,0,1,-1,-2,1,1,0,1,-1,-2,1,1,0,1,-1,-2,1,1,0,1,-1,-2,1,
               1,0,1,-1,-2
%N A101675 G.f.: (1-x-x^2)/(1+x^2+x^4).
%C A101675 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 04 2008: 
               (Start)
%C A101675 The sequence has a 12 term periodic cycle if indexed with offset 1, starting:
%C A101675 (1, 1, 0, -1, -1, -2, -1, -1, 0, 1, 1, 2,...(repeat)); such that even 
               terms =
%C A101675 2*Cos(n*Pi/6) and odds = (2/(sqrt3))*Cos(n*Pi/6). (End)
%H A101675 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A101675 a(0) = 1, a(1) = -1, a(2) = -2, a(3) = 1; for n >= 4, a(n)=-a(n-2)-a(n-4).
%F A101675 a(n)=sum{k=0..floor(n/2), (-1)^A010060(n-2k)*mod(binomial(n-k, k), 2)(-1)^k}; 
               a(n)=cos(2*pi*n/3+pi/6)/sqrt(3)+sin(2*pi*n/3+pi/6)+cos(pi*n/3+pi/
               3)-sin(pi*n/3+pi/3)/sqrt(3).
%Y A101675 Partial sums are A101676.
%Y A101675 Sequence in context: A075685 A037906 A120936 this_sequence A051764 A025906 
               A020944
%Y A101675 Adjacent sequences: A101672 A101673 A101674 this_sequence A101676 A101677 
               A101678
%K A101675 easy,sign
%O A101675 0,3
%A A101675 Paul Barry (pbarry(AT)wit.ie), Dec 11 2004

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