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 A101677 #18 Sep 08 2022 08:45:16
%S A101677 1,1,-1,-2,-2,-2,-1,-1,-3,-4,-4,-4,-3,-3,-5,-6,-6,-6,-5,-5,-7,-8,-8,
%T A101677 -8,-7,-7,-9,-10,-10,-10,-9,-9,-11,-12,-12,-12,-11,-11,-13,-14,-14,
%U A101677 -14,-13,-13,-15,-16,-16,-16,-15,-15,-17,-18,-18,-18,-17,-17,-19,-20,-20,-20,-19,-19,-21,-22,-22,-22,-21,-21,-23,-24,-24,-24,-23,-23,-25,-26,-26,-26,-25,-25,-27
%N A101677 a(n) = a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6).
%C A101677 Partial sums of A101676, second partial sums of A101675.
%H A101677 G. C. Greubel, <a href="/A101677/b101677.txt">Table of n, a(n) for n = 0..10000</a>
%H A101677 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-1)
%F A101677 G.f.: (1-x-x^2)/((1-x)^2*(1+x^2+x^4)).
%F A101677 a(n) = 2*sqrt(3)*sin(2*Pi*n/3)/9 + cos(Pi*n/3) + sin(Pi*n/3)/sqrt(3) - n/3.
%F A101677 a(3*(n+1)) = -A014681(n+1); a(3*n) = a(3*n+1) = 0^n -A014681(n); a(3*n+2) = -(n+1).
%t A101677 LinearRecurrence[{2, -2, 2, -2, 2, -1},{1, 1, -1, -2, -2, -2},81] (* _Ray Chandler_, Sep 03 2015 *)
%t A101677 CoefficientList[Series[(1-x-x^2)/((1-x)^2(1+x^2+x^4)),{x,0,80}],x] (* _Harvey P. Dale_, Dec 02 2021 *)
%o A101677 (PARI) x='x+O('x^100); Vec((1-x-x^2)/((1-x)^2*(1+x^2+x^4))) \\ _G. C. Greubel_, Sep 07 2018
%o A101677 (Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x-x^2)/((1-x)^2*(1+x^2+x^4)))); // _G. C. Greubel_, Sep 07 2018
%K A101677 easy,sign
%O A101677 0,4
%A A101677 _Paul Barry_, Dec 11 2004