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%I #34 May 09 2021 11:17:57
%S 4,0,216,5104,13896,161568,1259712,2016496,2562624,14926248,58995000,
%T 34012224,150547032,471960000,119095488,1259712000,952763904,
%U 5159780352,3974344704,2176782336,10077696000,2985984000,36330467328,30723115968,23887872000,17414258688,72825163776,75686967000
%N Smallest number that is the sum of 3 nonnegative cubes in exactly n ways.
%e a(0) = 4 because the smallest number that cannot be represented as a sum of 3 nonnegative cubes is 4.
%e a(1) = 0 is the sum of three 0's.
%e a(2) = 216 = 3^3 + 4^3 + 5^3 = 6^3 + 0 + 0.
%e a(3) = 5104 = 1 + 12^3 + 15^3 = 2^3 + 10^3 + 16^3 = 9^3 + 10^3 + 15^3.
%o (Python)
%o TOP = 6000000
%o a = [0]*TOP
%o for b in range(TOP):
%o b3 = b**3
%o if b3*3>=TOP: break
%o for c in range(b,TOP):
%o c3 = b3 + c**3
%o if c3>=TOP: break
%o for d in range(c,TOP):
%o res = c3 + d**3
%o if res>=TOP: break
%o a[res] += 1
%o m = max(a)
%o r = [-1] * (m+1)
%o for i in range(TOP):
%o if r[a[i]]==-1: r[a[i]]=i
%o print(r)
%Y Cf. A000578, A000446, A011541, A025418, A025419.
%K nonn
%O 0,1
%A _Alex Ratushnyak_, Feb 25 2015
%E More terms from _Rémy Sigrist_, Jul 14 2020
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