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 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 (list; graph; refs; listen; history; text; internal format)
 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 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, 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 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 STATUS approved

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Last modified June 20 17:30 EDT 2021. Contains 345189 sequences. (Running on oeis4.)