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 A309020 #6 Jul 06 2019 20:59:08
%S A309020 0,1,1,2,1,2,2,2,1,1,2,3,2,2,2,1,1,0,1,2,2,4,3,3,2,1,2,2,2,1,1,0,1,0,
%T A309020 0,0,1,3,2,3,2,4,4,5,3,2,3,2,2,0,1,1,2,3,2,2,2,1,1,0,1,0,0,0,1,1,0,-1,
%U A309020 0,0,0,1,1,4,3,4,2,2,3,3,2,3,4,6,4,5,5,4,3,0,2
%N A309020 Expansion of x * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+1)) - x^(2^(k+2))).
%F A309020 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n) + a(n+1) - a(n-1).
%t A309020 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 A309020 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 A309020 Cf. A002487, A005590, A309019, A309021, A309022.
%K A309020 sign
%O A309020 0,4
%A A309020 _Ilya Gutkovskiy_, Jul 06 2019