This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A103368 #21 Jan 18 2025 01:57:11
%S A103368 1,1,-1,-1,0,0,1,1,-1,-1,0,0,1,1,-1,-1,0,0,1,1,-1,-1,0,0,1,1,-1,-1,0,
%T A103368 0,1,1,-1,-1,0,0,1,1,-1,-1,0,0,1,1,-1,-1,0,0,1,1,-1,-1,0,0,1,1,-1,-1,
%U A103368 0,0,1,1,-1,-1,0,0,1,1,-1,-1,0,0,1,1,-1,-1,0,0,1,1,-1,-1,0,0
%N A103368 Period 6: repeat [1, 1, -1, -1, 0, 0].
%C A103368 The positive sequence is A131719(n+1) = a(n) = cos(2*Pi*n/3+Pi/3)/6 + sqrt(3)*sin(2*Pi*n/3+Pi/3)/6 - sqrt(3)*cos(Pi*n/3+Pi/6)/6 + sin(Pi*n/3+Pi/6)/2 + 2/3, with g.f. (1+x^2) / ( (1-x)*(1-x+x^2)*(1+x+x^2) ).
%H A103368 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,0,-1).
%F A103368 G.f.: (1+x)/(1+x^2+x^4).
%F A103368 a(n) = Sum_{k=0..floor(n/2)} binomial(k, floor(n/2)-k)*(-1)^k.
%F A103368 a(n) = -cos(2*Pi*n/3+Pi/3)/2 + sqrt(3)*sin(2*Pi*n/3+Pi/3)/6 + sqrt(3)*cos(Pi*n/3+Pi/6)/2 + sin(Pi*n/3+Pi/6)/2.
%F A103368 a(n) = cos(Pi*n/3) + sin(2*Pi*n/3)/sqrt(3). - _R. J. Mathar_, Oct 08 2011
%F A103368 a(n) + a(n-2) + a(n-4) = 0 for n>3. - _Wesley Ivan Hurt_, Jun 20 2016
%F A103368 E.g.f.: (sqrt(3)*sin(sqrt(3)*x/2) + 3*cos(sqrt(3)*x/2)*exp(x))*exp(-x/2)/3. - _Ilya Gutkovskiy_, Jun 21 2016
%p A103368 A103368:=n->[1, 1, -1, -1, 0, 0][(n mod 6)+1]: seq(A103368(n), n=0..100); # _Wesley Ivan Hurt_, Jun 20 2016
%t A103368 PadRight[{}, 100, {1, 1, -1, -1, 0, 0}] (* _Wesley Ivan Hurt_, Jun 20 2016 *)
%o A103368 (Magma) &cat [[1, 1, -1, -1, 0, 0]^^20]; // _Wesley Ivan Hurt_, Jun 20 2016
%Y A103368 Cf. A131719.
%K A103368 easy,sign
%O A103368 0,1
%A A103368 _Paul Barry_, Feb 02 2005