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 A320042 #38 Sep 01 2020 13:41:20
%S A320042 0,-1,1,0,-2,0,2,1,-1,-3,-1,1,-1,1,3,2,0,-2,0,-2,-4,-2,0,2,0,-2,0,2,0,
%T A320042 2,4,3,1,-1,1,-1,-3,-1,1,-1,-3,-5,-3,-1,-3,-1,1,3,1,-1,1,-1,-3,-1,1,3,
%U A320042 1,-1,1,3,1,3,5,4,2,0,2,0,-2,0,2,0,-2,-4,-2,0,-2,0,2,0
%N A320042 a(n) = a(floor(n/2)) + (-1)^(n*(n+1)/2) with a(1)=0.
%C A320042 For 2^(2*k-1) - 1 < n < 2^(2*k), k>0, there's no n such that a(n)=0.
%C A320042 For 2^(2*k) - 1 < n < 2^(2*k+1), k>0, there are A000984(k+1) n's such that a(n)=0.
%H A320042 Robert Israel, <a href="/A320042/b320042.txt">Table of n, a(n) for n = 1..10000</a>
%F A320042 a(1) = 0, a(n) = a(floor(n/2)) + (-1)^(n*(n+1)/2).
%F A320042 a(n) = 2*A092339(n+1) - A000523(n).
%e A320042 a(9) = a(4) + (-1)^45 = -1, a(10) = a(5) + (-1)^55 = -3.
%e A320042 For 7 < n < 16, there's no n such that a(n)=0; for 15 < n < 32, there are 6 n's such that a(n)=0.
%p A320042 a:=proc(n) `if`(n=1,0,a(floor(n/2))+(-1)^(n*(n+1)/2)) end: seq(a(n),n=1..100); # _Muniru A Asiru_, Oct 07 2018
%t A320042 a[1] = 0; a[n_] := a[n] = a[Floor[n/2]] + (-1)^(n*(n + 1)/2); Table[a@n, {n, 1, 50}]
%o A320042 (PARI) a(n) = if (n==1, 0, a(n\2) + (-1)^(n*(n+1)/2)); \\ _Michel Marcus_, Oct 05 2018
%Y A320042 Cf. A000523, A000984, A007088, A092339.
%K A320042 sign,look,hear
%O A320042 1,5
%A A320042 _Jinyuan Wang_, Oct 03 2018
%E A320042 More terms from _Michel Marcus_, Oct 05 2018