A281488 a(n) = -Sum_{d divides (n-2), 1 <= d < n} a(d).

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, -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, 13, 0, -17, 1, 18, -2, -17, 1, 17, 0, -24, 0, 28, -1, -21, 0, 22

Offset: 1

Author

Andrey Zabolotskiy, Jan 22 2017

Keywords

• sign
• easy
• look
• hear

Comments

a(1) = 1, any other choice simply adds a factor to all terms.

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.

Links

• Andrey Zabolotskiy, Table of n, a(n) for n = 1..20000
• Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, Involve, 15 (2022), 251-270; arXiv preprint, arXiv:2012.04625 [math.CO], 2020-2021.

Crossrefs

Cf. A007439 (same formula with overall + instead of -), A281487 (same formula with (n-1) instead of (n-2)), A000123.

Programs

Python

a = [1]
for n in range(2, 100):
   a.append(-sum(a[d-1] for d in range(1, n) if (n-2)%d == 0))
print(a)

Formula

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