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A350861
Number of solutions to +-1^3 +- 2^3 +- 3^3 +- ... +- n^3 = 0 or 1.
3
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 1, 4, 2, 6, 1, 4, 124, 12, 344, 536, 712, 1140, 713, 4574, 2260, 4384, 5956, 10634, 73758, 48774, 197767, 406032, 638830, 1147500, 1097442, 4249160, 3263500, 6499466, 11844316, 21907736, 82561050, 85185855, 261696060
OFFSET
0,11
LINKS
EXAMPLE
a(12) = 2: +1^3 + 2^3 - 3^3 + 4^3 - 5^3 - 6^3 - 7^3 + 8^3 + 9^3 - 10^3 - 11^3 + 12^3 = -1^3 - 2^3 + 3^3 - 4^3 + 5^3 + 6^3 + 7^3 - 8^3 - 9^3 + 10^3 + 11^3 - 12^3 = 0.
MAPLE
f:= proc(n) local S, k, x, s;
S:= mul(1 + x^(2*k^3), k=1..n);
s:= sum(k^3, k=1..n);
coeff(S, x, s) + coeff(S, x, s+1)
end proc:
map(f, [$0..50]); # Robert Israel, Mar 15 2023
PROG
(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(0, n) + b(1, n)
print([a(n) for n in range(46)]) # Michael S. Branicky, Jan 19 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 19 2022
STATUS
approved