A151761 G.f.: Theta^5, where Theta = Sum_{k>=0} x^(2^k).

0, 0, 0, 0, 0, 1, 5, 10, 15, 25, 31, 30, 40, 50, 50, 60, 75, 65, 55, 70, 66, 70, 90, 100, 100, 90, 90, 100, 110, 100, 120, 120, 75, 65, 95, 70, 90, 110, 130, 100, 126, 110, 130, 140, 150, 140, 160, 120, 100, 90, 130, 100, 150, 140, 160, 120, 110, 100, 160, 120, 120, 120, 120

Offset: 0

Author

N. J. A. Sloane, Jun 22 2009

Keywords

• nonn

Comments

Number of ways to write n as an ordered sum of 5 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), A151759 (m=3), A151760 (m=4), this sequence (m=5), A151762 (m=6).

Cf. 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, 5):
seq(a(n), n=0..62);  # 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, 5];
Table[a[n], {n, 0, 62}] (* Jean-François Alcover, Apr 25 2022, after Alois P. Heinz *)