A281488 - OEIS

%I #36 Jun 11 2024 22:03:56

%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; <a href="https://arxiv.org/abs/2012.04625">arXiv preprint</a>, arXiv:2012.04625 [math.CO], 2020-2021.

%F a(1) = 1, a(n) = -Sum_{d|(n-2), 1 <= d < n} a(d) for n>1.

%o (Python)

%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