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

0,9

Links

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

Example

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

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

Prog

(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(0<s && s<=n, v[s]++); , 1); concat(1, v) \\ David A. Corneth, Jan 23 2025

Crossrefs

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

Sequence in context: A339184 A156839 A172299 * A377384 A094215 A329040

Adjacent sequences: A025450 A025451 A025452 * A025454 A025455 A025456

Keyword

nonn

Author

David W. Wilson

Status

approved