A001239 -id:A001239 - cp's OEIS frontend

A025465 Number of partitions of n into 3 distinct nonnegative cubes.

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

Offset: 0

David W. Wilson

nonn

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

			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)

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

Cf. A025468, A025469, A001239.

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 *)

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

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

A003998 Numbers that are a sum of distinct positive cubes in more than one way.

Original entry on oeis.org

216, 217, 224, 225, 540, 559, 560, 567, 568, 728, 729, 736, 737, 756, 757, 764, 793, 801, 820, 828, 854, 855, 862, 863, 881, 882, 889, 890, 918, 919, 926, 927, 945, 946, 953, 954, 980, 981, 1008, 1009, 1036, 1044, 1045, 1071, 1072, 1073, 1079, 1080

Offset: 1

N. J. A. Sloane

Zak Seidov and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..1038 from Zak Seidov)

Cf. A001239.

F:= proc(x,y) option remember;
  if y = 0 then 1
  elif y < x^3 then 0
  elif y = x^3 then 1
  else procname(x+1,y) + procname(x+1,y-x^3)
  fi
end proc:
select(t -> F(1,t) > 1, [$1..10000]); # Robert Israel, Dec 31 2015

ok[n_] := Length[ Select[ Union[ Union /@ Flatten[ Table[ DeleteCases[ PowersRepresentations[n, k, 3], 0, 2], {k, 1, Floor[(n-1)^(1/3)]}], 1]], Total[#^3] == n & , 2]] == 2; Reap[ Do[ If[ ok[n], Print[n]; Sow[n]], {n, 1, 1100}]][[2, 1]](* Jean-François Alcover, Feb 23 2012 *)

More terms from Larry Reeves (larryr(AT)acm.org), Mar 20 2000

A219329 Numbers that can be expressed as the sum of three nonnegative cubes in three ways.

Original entry on oeis.org

5104, 5832, 9288, 9729, 10261, 10773, 12104, 12221, 12384, 14175, 17604, 17928, 19034, 20691, 21412, 21888, 24416, 24480, 28792, 29457, 30528, 31221, 32850, 34497, 35216, 36288, 38259, 39339, 39376, 39528, 40060, 40097, 40832, 40851, 41033, 41040, 41364

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, Apr 11 2013

nonn

Index of A051343 = 9, superset of index of A025456 = 3.

Subset of A001239.

			a(1) = 5104 = 1^3+12^3+15^3 = 2^3+10^3+16^3 = 9^3+10^3+15^3.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Decomposition of the first 10000 terms into 3 sets of cube triples
Sequences related to sums of squares and cubes

Other sums of cubes: A025402, A025398, A024974, A001239, A008917.
Cf. A025456, A051343.
Cf. A025396.

Select[Range[42000],Length[PowersRepresentations[#,3,3]]==3&] (* Harvey P. Dale, Sep 28 2016 *)

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A025465 Number of partitions of n into 3 distinct nonnegative cubes.

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A003998 Numbers that are a sum of distinct positive cubes in more than one way.

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A219329 Numbers that can be expressed as the sum of three nonnegative cubes in three ways.

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Mathematica