A025465 - OEIS

%I #32 Jan 26 2024 11:28:21

%S 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,

%T 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,

%U 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

%N Number of partitions of n into 3 distinct nonnegative cubes.

%C 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

%H Antti Karttunen, <a href="/A025465/b025465.txt">Table of n, a(n) for n = 0..17073</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

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

%e From _Antti Karttunen_, Aug 29 2017: (Start)

%e For n = 9 there is one solution: 9 = 2^3 + 1^3 + 0^3, thus a(9) = 1.

%e 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.

%e (End)

%e From _Harvey P. Dale_, Sep 30 2018: (Start)

%e 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.

%e The first two numbers to attain the value of 3 are 5104 and 9729.

%e There are no numbers up to 10000 that attain a value greater than 3.

%e (End)

%t 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 *)

%o (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

%Y Cf. A025468, A025469, A001239.

%K nonn

%O 0,856

%A _David W. Wilson_