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 A339422 #11 Oct 22 2021 11:36:05
%S A339422 1,-1,0,1,-2,2,0,-3,4,-2,-2,6,-6,0,8,-11,4,10,-20,14,10,-36,38,-2,-54,
%T A339422 84,-46,-56,152,-144,-8,221,-316,146,244,-570,482,120,-876,1110,-350,
%U A339422 -1108,2138,-1520,-896,3548,-3914,566,4906,-8068,4714,4864,-14080,13652,466,-20656
%N A339422 G.f.: 1 / (1 + Sum_{k>=0} x^(2^k)).
%C A339422 The difference between the number of compositions (ordered partitions) of n into an even number of powers of 2 and the number of compositions (ordered partitions) of n into an odd number of powers of 2.
%H A339422 Alois P. Heinz, <a href="/A339422/b339422.txt">Table of n, a(n) for n = 0..5000</a>
%H A339422 Paul Barry, <a href="https://arxiv.org/abs/2107.00442">Conjectures and results on some generalized Rueppel sequences</a>, arXiv:2107.00442 [math.CO], 2021.
%F A339422 G.f. A(x) satisfies: A(x) = A(x^2) / (1 + x * A(x^2)).
%F A339422 a(0) = 1; a(n) = -Sum_{k=1..n} A209229(k) * a(n-k).
%p A339422 b:= proc(n, t) option remember; `if`(n=0, t,
%p A339422 add(b(n-2^i, -t), i=0..ilog2(n)))
%p A339422 end:
%p A339422 a:= n-> b(n, 1):
%p A339422 seq(a(n), n=0..60); # _Alois P. Heinz_, Dec 03 2020
%t A339422 nmax = 55; CoefficientList[Series[1/(1 + Sum[x^(2^k), {k, 0, Floor[Log[2, nmax]] + 1}]), {x, 0, nmax}], x]
%t A339422 a[0] = 1; a[n_] := a[n] = -Sum[If[IntegerQ[Log[2, k]], 1, 0] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 55}]
%Y A339422 Cf. A000079, A023359, A104977, A209229.
%K A339422 sign
%O A339422 0,5
%A A339422 _Ilya Gutkovskiy_, Dec 03 2020