A369875 - OEIS

%I #10 Feb 05 2024 20:57:20

%S 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,

%T 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,

%U 1,3,1,1,27,1,1,1,23,1,1943,1,1,1,1,1,20,1,225

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

%C 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.

%H Alois P. Heinz, <a href="/A369875/b369875.txt">Table of n, a(n) for n = 1..20000</a>

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

%o (Python)

%o from collections import Counter

%o from sympy import divisors

%o def A369875(n):

%o     c = {0:1}

%o     for d in divisors(n,generator=True):

%o         b = Counter(c)

%o         for j in c:

%o             a = c[j]

%o             b[j+d] += a

%o             b[j-d] += a

%o         c = b

%o     return c[n] # _Chai Wah Wu_, Feb 05 2024

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

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Feb 03 2024