A023358 Number of compositions into sums of cubes.

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 36, 44, 53, 64, 78, 96, 120, 150, 187, 232, 286, 351, 430, 527, 649, 802, 993, 1230, 1522, 1880, 2318, 2854, 3514, 4330, 5341, 6594, 8145, 10061, 12423, 15330, 18908, 23316, 28753, 35467, 43762, 54010, 66665, 82281, 101540, 125286, 154566, 190682

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 501 terms from T. D. Noe)

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      `if`(n<0, 0, add(a(n-i^3), i=1..iroot(n, 3))))
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Sep 08 2014

Mathematica

a[n_] := a[n] = If[n==0, 1, If[n<0, 0, Sum[a[n-i^3], {i, 1, Floor[n^(1/3)]}]]]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Apr 08 2015, after Alois P. Heinz *)

PARI

E=6; N=E^3-1; q='q+O('q^N);
gf=1/(1 - sum(n=1,E, q^(n^3) ) );  \\ test, several similar seqs.
v=Vec(gf) \\ Joerg Arndt, Mar 30 2014

Formula

G.f.: 1 / (1 - Sum_{n>=1} x^(n^3) ). - Joerg Arndt, Mar 30 2014

a(n) ~ c * d^n, where d = 1.2338881403372741887535479..., c = 0.418031200641837887398653... - Vaclav Kotesovec, May 01 2014