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

Author

Alois P. Heinz, Mar 06 2020

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A003714, A073266.

Programs

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 *)

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