A369875 a(n) = [x^n] Product_{d|n} (x^d + 1 + 1/x^d).

1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 11, 1, 11, 1, 1, 1, 85, 1, 1, 1, 6, 1, 64, 1, 1, 1, 1, 1, 145, 1, 1, 1, 54, 1, 41, 1, 1, 5, 1, 1, 382, 1, 1, 1, 1, 1, 34, 1, 34, 1, 1, 1, 2425, 1, 1, 3, 1, 1, 27, 1, 1, 1, 23, 1, 1943, 1, 1, 1, 1, 1, 20, 1, 225

Offset

1,6

Comments

a(n) is the number of solutions to n = Sum_{d|n} c_i * d with c_i in {-1,0,1}, i=1..tau(n), tau = A000005.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Mathematica

Table[Coefficient[Product[(x^d + 1 + 1/x^d), {d, Divisors[n]}], x, n], {n, 1, 80}]

Prog

(Python)
from collections import Counter
from sympy import divisors
def A369875(n):
    c = {0:1}
    for d in divisors(n, generator=True):
        b = Counter(c)
        for j in c:
            a = c[j]
            b[j+d] += a
            b[j-d] += a
        c = b
    return c[n] # Chai Wah Wu, Feb 05 2024

Crossrefs

Cf. A000005, A033630, A083206, A316706, A369874.

Sequence in context: A293768 A046564 A046592 * A334432 A370130 A010326

Adjacent sequences: A369872 A369873 A369874 * A369876 A369877 A369878

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 03 2024

Status

approved