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

Author

David W. Wilson

Keywords

• nonn

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

Examples

			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)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..100080
• Wikipedia, 1729 (number)

Crossrefs

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

Programs

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

Formula

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

Extensions

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