A333047 Number of compositions of 2n into n powers of 2.

1, 1, 1, 4, 13, 31, 76, 218, 645, 1849, 5281, 15346, 44980, 131704, 385568, 1131874, 3331429, 9819405, 28977079, 85633438, 253424053, 750895163, 2227288196, 6613217348, 19654450476, 58463536356, 174041552556, 518488451716, 1545686334184, 4610827520500

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2078

Formula

a(n) = A073266(2n,n).

a(n) mod 2 = 1 <=> n in { A003714 }.

a(n) ~ c * d^n / sqrt(n), where d = 3.03557496500556374352187743150809307334142929675774277... and c = 0.257758082536856928607441503594486605201517917904563... - Vaclav Kotesovec, Mar 10 2020

Example

a(3) = 4: 222, 114, 141, 411.
a(4) = 13: 2222, 1124, 1142, 1214, 1241, 1412, 1421, 2114, 2141, 2411, 4112, 4121, 4211.

Maple

b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
      `if`(t=0, 0, add(b(n-2^j, t-1), j=0..ilog2(n))))
    end:
a:= n-> b(2*n, n):
seq(a(n), n=0..30);

Mathematica

b[n_, t_] := b[n, t] = If[n == 0, If[t == 0, 1, 0], If[t == 0, 0, Sum[b[n - 2^j, t - 1], {j, 0, Floor@Log2[n]}]]];
a[n_] := b[2*n, n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 28 2022, after Alois P. Heinz *)

Crossrefs

Cf. A003714, A073266.

Sequence in context: A097122 A378850 A116411 * A376804 A106337 A027998

Adjacent sequences: A333044 A333045 A333046 * A333048 A333049 A333050

Keyword

nonn

Author

Alois P. Heinz, Mar 06 2020

Status

approved