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

0,4

Links

Table of n, a(n) for n=0..38.

Formula

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

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 *)

Crossrefs

Cf. A023359, A093659, A209229, A357476.

Sequence in context: A227208 A009854 A298116 * A018165 A054179 A010049

Adjacent sequences: A357531 A357532 A357533 * A357535 A357536 A357537

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 02 2022

Status

approved