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 A345008 #6 Jun 05 2021 16:44:57
%S A345008 1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,-1,0,0,0,1,1,1,1,0,1,1,1,0,1,1,1,-1,
%T A345008 0,0,0,1,1,1,1,0,1,1,1,0,1,1,1,-1,0,0,0,1,1,1,1,0,1,1,1,0,1,1,1,-2,-1,
%U A345008 -1,-1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,-1,0,0,0,1,1,1,1,0,1
%N A345008 a(0) = 1; a(4*n) = a(n) - a(n-1), a(4*n+1) = a(4*n+2) = a(4*n+3) = a(n).
%F A345008 G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3 - x^4) * A(x^4).
%F A345008 G.f.: Product_{k>=0} (1 + x^(4^k) + x^(2*4^k) + x^(3*4^k) - x^(4^(k+1))).
%t A345008 a[0] = 1; a[n_] := Switch[Mod[n, 4], 0, a[n/4] - a[(n - 4)/4], 1, a[(n - 1)/4], 2, a[(n - 2)/4], 3, a[(n - 3)/4]]; Table[a[n], {n, 0, 105}]
%t A345008 nmax = 105; A[_] = 1; Do[A[x_] = (1 + x + x^2 + x^3 - x^4) A[x^4] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A345008 nmax = 105; CoefficientList[Series[Product[(1 + x^(4^k) + x^(2 4^k) + x^(3 4^k) - x^(4^(k + 1))), {k, 0, Floor[Log[4, nmax]] + 1}], {x, 0, nmax}], x]
%Y A345008 Cf. A005590, A277872, A309048, A345009.
%K A345008 sign
%O A345008 0,65
%A A345008 _Ilya Gutkovskiy_, Jun 05 2021