cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A025463 Number of partitions of n into 10 positive cubes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 0, 1, 0
Offset: 0

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Keywords

Crossrefs

Cf. A000578 (cubes).
Column k=10 of A320841.

Programs

  • Maple
    b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
          `if`(i<1 or t<1, 0, b(n, i-1, t)+
          `if`(i^3>n, 0, b(n-i^3, i, t-1))))
        end:
    a:= n-> b(n, iroot(n, 3), 10):
    seq(a(n), n=0..120);  # Alois P. Heinz, Dec 21 2018
  • Mathematica
    b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] + If[i^3 > n, 0, b[n - i^3, i, t - 1]]]];
    a[n_] := b[n, n^(1/3) // Floor, 10];
    a /@ Range[0, 120] (* Jean-François Alcover, Dec 04 2020, after Alois P. Heinz *)
    Table[Count[IntegerPartitions[n,{10}],?(AllTrue[CubeRoot[#],IntegerQ]&)],{n,0,110}] (* _Harvey P. Dale, Jul 26 2025 *)

Formula

a(n) = [x^n y^10] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019