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

0,9

Links

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

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A005710 A367800 A291146 * A322855 A322803 A322800

Adjacent sequences: A023355 A023356 A023357 * A023359 A023360 A023361

Keyword

nonn

Author

David W. Wilson

Status

approved