A025466 Number of partitions of n into 4 distinct nonnegative cubes.

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, 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, 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

Offset

0,541

Comments

In other words, number of solutions to the equation n = w^3 + x^3 + y^3 + z^3 with w > x > y > z >= 0. - Antti Karttunen, Sep 21 2018

Links

Antti Karttunen, Table of n, a(n) for n = 0..12121

Example

For n=540 we have two solutions: 540 = (0^3 + 1^3 + 3^3 + 8^3) = (2^3 + 4^3 + 5^3 + 7^3), thus a(540) = 2. This is the first point where a(n) > 1. - Antti Karttunen, Sep 21 2018

Prog

(PARI) A025466(n) = { my(s=0); for(w=0, n, if(ispower(w, 3), for(x=w+1, n-w, if(ispower(x, 3), for(y=x+1, n-(w+x), if(ispower(y, 3), for(z=y+1, n-(w+x+y), if((ispower(z, 3)&&(w+x+y+z)==n), s++)))))))); (s); }; \\ Antti Karttunen, Sep 21 2018

Crossrefs

Cf. A000578, A025465.

Sequence in context: A378651 A023976 A025469 * A072769 A353625 A379958

Adjacent sequences: A025463 A025464 A025465 * A025467 A025468 A025469

Keyword

nonn

Author

David W. Wilson

Extensions

Secondary offset added by Antti Karttunen, Sep 21 2018

Status

approved