A378171 Number of subsets of the first n positive cubes whose sum is a positive cube.

1, 2, 3, 4, 6, 7, 8, 11, 12, 18, 23, 32, 42, 67, 99, 150, 247, 391, 635, 1098, 1865, 2927, 4932, 9109, 14825, 26926, 48452, 83758, 148387, 263258, 468595, 840912, 1559322, 2785642, 5146754, 9454946, 16756330, 31372080, 57754175, 105385375, 196773661, 368705288, 671572482

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..74

Example

a(8) = 11 subsets: {1}, {8}, {27}, {64}, {125}, {216}, {343}, {512}, {1, 216, 512}, {27, 64, 125} and {1, 27, 64, 125, 512}.

Prog

(Python)
from sympy import integer_nthroot
def is_cube(n): return integer_nthroot(n, 3)[1]
from functools import cache
@cache
def b(n, soc):
    if n == 0:
        if soc > 0 and is_cube(soc): return 1
        return 0
    return b(n-1, soc) + b(n-1, soc+n**3)
a = lambda n: b(n, 0)
print([a(n) for n in range(1, 30)]) # Michael S. Branicky, Nov 18 2024

Crossrefs

Cf. A000578, A126111, A336815, A339615, A378170.

Sequence in context: A352804 A102826 A191381 * A051602 A348469 A163866

Adjacent sequences: A378168 A378169 A378170 * A378172 A378173 A378174

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 18 2024

Extensions

a(25) and beyond from Michael S. Branicky, Nov 18 2024

Status

approved