A025465 Number of partitions of n into 3 distinct nonnegative cubes.

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

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Comments

In other words, number of solutions to the equation n = x^3 + y^3 + z^3 with x > y > z >= 0. - Antti Karttunen, Aug 29 2017

Examples

			From _Antti Karttunen_, Aug 29 2017: (Start)
For n = 9 there is one solution: 9 = 2^3 + 1^3 + 0^3, thus a(9) = 1.
For n = 855 there are two solutions: 855 = 9^3 + 5^3 + 1^3 = 8^3 + 7^3 + 0^3, thus a(855) = 2. This is also the first point where sequence attains value greater than one.
(End)
From _Harvey P. Dale_, Sep 30 2018: (Start)
In addition to 855, the following numbers attain the value of 2: 1009, 1072, 1366, 1457, and there are 73 more such numbers less than 10000.
The first two numbers to attain the value of 3 are 5104 and 9729.
There are no numbers up to 10000 that attain a value greater than 3.
(End)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..17073
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A025468, A025469, A001239.

Programs

Mathematica

Table[Length[FindInstance[{n==x^3+y^3+z^3,x>y>z>=0},{x,y,z},Integers,5]],{n,0,110}] (* Harvey P. Dale, Sep 30 2018 *)

PARI

A025465(n) = { my(s=0); for(x=0,n,if(ispower(x,3),for(y=x+1,n-x,if(ispower(y,3),for(z=y+1,n-(x+y),if((ispower(z,3)&&(x+y+z)==n),s++)))))); (s); }; \\ Antti Karttunen, Aug 29 2017

Formula

a(n) = A025468(n) + A025469(n).