A151762 G.f.: Theta^6, where Theta = Sum_{k>=0} x^(2^k).

0, 0, 0, 0, 0, 0, 1, 6, 15, 26, 45, 66, 76, 96, 126, 140, 165, 210, 221, 210, 240, 252, 246, 300, 346, 360, 366, 380, 396, 420, 440, 480, 525, 450, 405, 450, 416, 396, 510, 540, 510, 516, 582, 540, 636, 660, 720, 720, 706, 600, 630, 620, 636, 660, 800, 720, 756, 660, 720

Offset: 0

Author

N. J. A. Sloane, Jun 22 2009

Keywords

• nonn

Comments

Number of ways to write n as an ordered sum of 6 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), A151761 (m=5), this sequence (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, 6):
seq(a(n), n=0..58);  # 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, 6];
Table[a[n], {n, 0, 58}] (* Jean-François Alcover, Apr 25 2022, after Alois P. Heinz *)