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%I #26 Nov 16 2022 18:13:40
%S 1,-1,-1,0,0,0,-1,1,0,-1,0,1,-1,0,0,1,0,-2,-1,3,0,-2,1,2,-2,-3,1,4,-1,
%T -3,0,5,-1,-7,1,7,-1,-5,0,6,1,-9,-2,11,1,-9,-1,8,0,-12,0,15,0,-11,-1,
%U 13,0,-17,1,18,-2,-17,1,17,0,-24,0,28,-1,-21,0,22
%N a(n) = -Sum_{d divides (n-2), 1 <= d < n} a(d).
%C a(1) = 1, any other choice simply adds a factor to all terms.
%C The even bisection of the sequence seems to behave similarly to A281487 with similar asymptotics for |a(n)|. However, the odd bisection shows oscillations with increasing intervals between crossing the zero and increasing amplitude.
%H Andrey Zabolotskiy, <a href="/A281488/b281488.txt">Table of n, a(n) for n = 1..20000</a>
%H Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi and Ruimin Zhang, <a href="https://doi.org/10.2140/involve.2022.15.251">Finding structure in sequences of real numbers via graph theory: a problem list</a>, Involve, 15 (2022), 251-270; arXiv:<a href="https://arxiv.org/abs/2012.04625">2012.04625</a> [math.CO], 2020-2021.
%F a(1) = 1,
%F a(n) = -Sum_{d|(n-2), 1 <= d < n} a(d) for n>1.
%o a = [1]
%o for n in range(2, 100):
%o a.append(-sum(a[d-1] for d in range(1, n) if (n-2)%d == 0))
%o print(a)
%Y Cf. A007439 (same formula with overall + instead of -), A281487 (same formula with (n-1) instead of (n-2)), A000123.
%K sign,easy,look,hear
%O 1,18
%A _Andrey Zabolotskiy_, Jan 22 2017
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