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

0,5

Links

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

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}]

Crossrefs

Cf. A000045, A023359, A109696, A364526.

Sequence in context: A314464 A135455 A020712 * A369220 A364526 A182506

Adjacent sequences: A369219 A369220 A369221 * A369223 A369224 A369225

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 16 2024

Status

approved