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 A309021 #6 Jul 06 2019 20:59:01
%S A309021 0,1,1,0,1,-2,0,0,1,-3,-2,1,0,2,0,1,1,-4,-3,0,-2,6,1,1,0,1,2,-2,0,-1,
%T A309021 1,0,1,-6,-4,0,-3,7,0,1,-2,8,6,-3,1,-6,1,-2,0,0,1,1,2,-5,-2,0,0,1,-1,
%U A309021 2,1,0,0,0,1,-7,-6,1,-4,10,0,1,-3,10,7,-4,0,-6,1,-3,-2,9,8,0,6,-17,-3,-2,1,-4,-6
%N A309021 Expansion of x * Product_{k>=0} (1 + x^(2^k) - x^(2^(k+1)) - x^(2^(k+2))).
%F A309021 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n+1) - a(n) - a(n-1).
%t A309021 nmax = 90; CoefficientList[Series[x Product[(1 + x^(2^k) - x^(2^(k + 1)) - x^(2^(k + 2))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%t A309021 a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], a[(n + 1)/2] - a[(n - 1)/2] - a[(n - 3)/2]]; Table[a[n], {n, 0, 90}]
%Y A309021 Cf. A002487, A005590, A309019, A309020, A309022.
%K A309021 sign
%O A309021 0,6
%A A309021 _Ilya Gutkovskiy_, Jul 06 2019