A369222 Number of compositions (ordered partitions) of n into powers of 2 not greater than sqrt(n).

1, 1, 1, 1, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 4930, 8651, 15182, 26642, 46754, 82047, 143983, 252672, 443409, 778128, 1365520, 2396320, 4205249, 7379697, 12950466, 22726483, 39882198, 69988378, 122821042, 215535903, 378239143, 663763424

Offset: 0

Author

Ilya Gutkovskiy, Jan 16 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..4048

Crossrefs

Cf. A000045, A023359, A109696, A364526.

Programs

Maple

b:= proc(n, t) option remember; `if`(n=0, 1,
      add(b(n-2^j, t), j=0..min(ilog2(n), t)))
    end:
a:= n-> b(n, ilog2(floor(sqrt(n)))):
seq(a(n), n=0..37);  # Alois P. Heinz, Jan 18 2024

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[IntegerQ[Log[2, k]]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 37}]