A357534 Number of compositions (ordered partitions) of n into two or more powers of 2.

0, 0, 1, 3, 5, 10, 18, 31, 55, 98, 174, 306, 542, 956, 1690, 2983, 5271, 9310, 16448, 29050, 51318, 90644, 160118, 282826, 499590, 882468, 1558798, 2753448, 4863696, 8591212, 15175514, 26805983, 47350055, 83639030, 147739848, 260967362, 460972286, 814260544, 1438308328

Offset: 0

Author

Ilya Gutkovskiy, Oct 02 2022

Keywords

• nonn

Crossrefs

Cf. A023359, A093659, A209229, A357476.

Programs

Maple

b:= proc(n) option remember;
      `if`(n=0, 1, add(b(n-2^i), i=0..ilog2(n)))
    end:
a:= n-> b(n)-`if`(2^ilog2(n)=n, 1, 0):
seq(a(n), n=0..50);  # Alois P. Heinz, Oct 02 2022

Mathematica

b[n_] := b[n] = If[n == 0, 1, Sum[b[n - 2^i], {i, 0, Floor@ Log2[n]}]];
a[n_] :=  b[n] - If[2^Floor@Log2[n] == n, 1, 0];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Dec 26 2022, after Alois P. Heinz *)

Formula

a(n) = A023359(n) - A209229(n) for n > 0.