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 A117902 #9 Sep 08 2022 08:45:24
%S A117902 1,0,-1,2,0,-4,8,0,-16,32,0,-64,128,0,-256,512,0,-1024,2048,0,-4096,
%T A117902 8192,0,-16384,32768,0,-65536,131072,0,-262144,524288,0,-1048576,
%U A117902 2097152,0,-4194304,8388608,0,-16777216,33554432,0,-67108864,134217728,0,-268435456,536870912,0,-1073741824
%N A117902 Expansion of (1-x^2-2x^3)/(1-4x^3).
%C A117902 Row sums of number triangle A117901.
%H A117902 G. C. Greubel, <a href="/A117902/b117902.txt">Table of n, a(n) for n = 0..1000</a>
%H A117902 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4).
%F A117902 a(n) = 0^n/2 - (2^(2*n/3)/12)*( 2*cos((2*n+1)*Pi*n/3) + 2*sqrt(3)*sin((2*n+1)*Pi*n/3) -(2^(2/3) + 8)*cos(2*Pi*n/3) - 2^(1/6)*sqrt(6)*sin(2*Pi*n/3) + 2^(2/3) - 2 ).
%F A117902 a(n) = (1/2)*[n=0] + 2*A133851(n-3) - A133851(n-2). - _G. C. Greubel_, Oct 09 2021
%t A117902 LinearRecurrence[{0,0,4}, {1,0,-1,2}, 50] (* _G. C. Greubel_, Oct 09 2021 *)
%o A117902 (Magma) [1] cat [n le 3 select (-1)^(n-1)*(n-1) else 4*Self(n-3): n in [1..50]]; // _G. C. Greubel_, Oct 09 2021
%o A117902 (Sage)
%o A117902 def A133851(n): return 4^(n/3) if (n%3==0) else 0
%o A117902 def A117902(n): return bool(n==0)/2 + 2*A133851(n-3) - A133851(n-2)
%o A117902 [A117902(n) for n in (0..50)] # _G. C. Greubel_, Oct 09 2021
%Y A117902 Cf. A117901, A133851.
%K A117902 easy,sign
%O A117902 0,4
%A A117902 _Paul Barry_, Apr 01 2006