A348892 Number of solutions to +-1^3 +- 2^3 +- 3^3 +- ... +- n^3 = n.

1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 4, 0, 0, 83, 69, 0, 0, 353, 414, 0, 0, 7800, 12496, 0, 0, 48162, 56870, 0, 0, 733392, 1253467, 0, 0, 4892337, 10022277, 0, 0, 45859303, 149422926, 0, 0, 623257759, 1339056922, 0, 0, 7453502893, 13446831198

Offset: 0

Author

Ilya Gutkovskiy, Jan 28 2022

Keywords

• nonn

Crossrefs

Cf. A063890, A158118, A348165.

Programs

Python

from functools import lru_cache
@lru_cache(maxsize=None)
def b(n, i):
    if n > (i*(i+1)//2)**2: return 0
    if i == 0: return 1
    return b(n+i**3, i-1) + b(abs(n-i**3), i-1)
def a(n): return b(n, n)
print([a(n) for n in range(54)]) # Michael S. Branicky, Jan 28 2022

Formula

a(n) = [x^n] Product_{k=1..n} (x^(k^3) + 1/x^(k^3)).