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

Author

David W. Wilson

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

Maple

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

PARI

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