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A025465
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Number of partitions of n into 3 distinct nonnegative cubes.
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4
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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
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0,856
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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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)
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)
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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