A025446 Number of partitions of n into 2 nonnegative cubes.

1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1

Offset

0,1730

Comments

a(1729) = 2, the first point where a value larger than 1 appears, and where this sequence differs from A373972. - Antti Karttunen, Jun 24 2024

Links

Antti Karttunen, Table of n, a(n) for n = 0..100080

Wikipedia, 1729 (number)

Formula

a(n) = A010057(n) + A025455(n) = A010057(n) XOR A025455(n). [The latter by Fermat's Last Theorem] - Antti Karttunen, Jun 24 2024

Example

From Antti Karttunen, Jun 24 2024: (Start)
8 = 0^3 + 2^3, and as there are no other partitions of 8 into 2 nonnegative cubes, a(8) = 1.
16 = 2^3 + 2^3, and as there are no other partitions of 16 into 2 nonnegative cubes, a(16) = 1.
1729 = 1^3 + 12^3 = 9^3 + 10^3, and as there are no other partitions of 1729 into 2 nonnegative cubes, a(1729) = 2.
(End)

Prog

(PARI) A025446(n) = if(n<=2, 1, my(s=0, x=sqrtnint(n, 3)); forstep(i=x, 0, -1, my(x3=i^3, y3=n-x3); if(y3>x3, return(s), s += ispower(y3, 3)))); \\ Antti Karttunen, Jun 24 2024

Crossrefs

Cf. A010057, A025455, A004999 (indices of nonzero terms), A373972 (their characteristic function).

Sequence in context: A371690 A179830 A266216 * A373972 A266300 A266605

Adjacent sequences: A025443 A025444 A025445 * A025447 A025448 A025449

Keyword

nonn

Author

David W. Wilson

Extensions

Data section extended up to a(126) and the secondary offset added by Antti Karttunen, Jun 24 2024

Status

approved