A224214 Number of nonnegative solutions to x^3 + y^3 <= n^3.

1, 3, 6, 11, 18, 26, 37, 50, 63, 80, 96, 115, 136, 159, 186, 210, 239, 268, 301, 336, 368, 407, 444, 487, 526, 574, 619, 664, 717, 764, 820, 875, 930, 989, 1047, 1112, 1175, 1238, 1307, 1375, 1444, 1521, 1592, 1669, 1745, 1828, 1907, 1988, 2073, 2161, 2252

Offset: 0

Author

Alex Ratushnyak, Apr 01 2013

Keywords

• nonn

Programs

PARI

a(n) = n++; p = Pol((1/(1 - x))*sum(k=0, n, x^(k^3))^2 + O(x^(n^3))); polcoeff(p, (n-1)^3); \\ Michel Marcus, Apr 21 2018

Python

for a in range(99):
  n = a*a*a
  k = 0
  for x in range(99):
    s = x*x*x
    if s>n: break
    for y in range(99):
        sy = s + y*y*y
        if sy>n: break
        k+=1
  print(str(k), end=',')

Formula

a(n) = [x^(n^3)] (1/(1 - x))*(Sum_{k>=0} x^(k^3))^2. - Ilya Gutkovskiy, Apr 20 2018