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
Keywords
Programs
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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 *)