A151759 G.f.: Theta^3, where Theta = Sum_{k>=0} x^(2^k).

0, 0, 0, 1, 3, 3, 4, 6, 3, 3, 6, 6, 4, 6, 6, 0, 3, 3, 6, 6, 6, 6, 6, 0, 4, 6, 6, 0, 6, 0, 0, 0, 3, 3, 6, 6, 6, 6, 6, 0, 6, 6, 6, 0, 6, 0, 0, 0, 4, 6, 6, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 3, 3, 6, 6, 6, 6, 6, 0, 6, 6, 6, 0, 6, 0, 0, 0, 6, 6, 6, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 6, 6, 0, 6, 0, 0, 0, 6

Offset: 0

Author

N. J. A. Sloane, Jun 22 2009

Keywords

• nonn

Comments

Number of ways to write n as an ordered sum of 3 powers of 2. - Ilya Gutkovskiy, Feb 02 2021

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

(Sum_{k>=0} x^(2^k))^m; A209229 (m=1), A073267 (m=2), this sequence (m=3), A151760 (m=4), A151761 (m=5), A151762 (m=6).

Cf. A000079, A151758.

Programs

Maple

b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
      `if`(t<1, 0, add(b(n-2^j, t-1), j=0..ilog2(n))))
    end:
a:= n-> b(n, 3):
seq(a(n), n=0..104);  # Alois P. Heinz, Feb 02 2021

Mathematica

b[n_, t_] := b[n, t] = If[n == 0, If[t == 0, 1, 0],
     If[t < 1, 0, Sum[b[n - 2^j, t - 1], {j, 0, Floor@Log2[n]}]]];
a[n_] := b[n, 3];
Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Mar 08 2022, after Alois P. Heinz *)