A025454 -id:A025454 - cp's OEIS frontend

A025453 Number of partitions of n into 9 nonnegative cubes.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 4, 2, 2, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 3, 2, 2, 3, 2, 4, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 2, 3

Offset: 0

David W. Wilson

nonn

			a(8) = 2 via 8*0^3 + 1*2^3 = 1 * 0^3 + 8*1^3.

David A. Corneth, Table of n, a(n) for n = 0..10000

Cf. A025446, A025447, A025448, A025449, A025450, A025451, A025452, this sequence, A025454.

f:= proc(x,m,M)
local i;
option remember;
  if x = 0 then return 1
  elif m = 0 then return 0
  fi;
  add(procname(x-i^3, m-1, i), i=1..min(M,floor(x^(1/3))));
end proc:
map(f, [$0..150],9,150); # Robert Israel, Jan 23 2025

first(n) = my(v=vector(n), maxb=sqrtnint(n, 3)); forvec(x=vector(9, i, [0, maxb]), s=sum(i=1, 9, x[i]^3); if(0David A. Corneth, Jan 23 2025

a(n) = {my(res = 0); res=aIterate(n^3, 1, n); res } aIterate(s, m, q) = { if(s == 0, return(1)); if(q == 0, return(0)); sum(i = m, sqrtnint(s, 3), aIterate(s - i^3, i, q-1) ) } \\ David A. Corneth, Sep 23 2019

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A025453 Number of partitions of n into 9 nonnegative cubes.

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A307738 Number of partitions of n^3 into at most n cubes.