

A025465


Number of partitions of n into 3 distinct nonnegative cubes.


4



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
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OFFSET

0,1


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


LINKS

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


FORMULA

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


EXAMPLE

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)


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 *)


PROG

A025465(n) = { my(s=0); for(x=0, n, if(ispower(x, 3), for(y=x+1, nx, 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


CROSSREFS

Cf. A025468, A025469, A001239.
Sequence in context: A297039 A239705 A025468 * A323514 A302047 A044940
Adjacent sequences: A025462 A025463 A025464 * A025466 A025467 A025468


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



