A349552 a(n) is the number of halving partitions of n (see Comments for definition).

1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 1, 3, 2, 2, 1

Offset

1,5

Comments

Let S(m) = {f(m/2)), c(m/2) : m >= 1}, where f = floor and c = ceiling. A halving partition of n is a partition p(1) + p(2) + ... + p(k) of n such that p(1) is in S(n) and p(i) is in S(p(i-1)) for i = 1, 2, ..., k. The basic idea is that each term after the first is about half of the preceding term.

Links

Table of n, a(n) for n=1..16.

Example

a(9) counts these 2 partitions:
c(9/2) + f(5/2) + f(2/2} + c(1/2) = 5 + 3 + 1;
f(9/2) + f(5/2) + f(2/2) + c(1/2) = 4 + 2 + 1 + 1.
a(13) counts these:
c(13/2) + c(7/2) + f(4/2) = 7 + 4 + 2;
c(13/2) + f(7/2) + c(3/2) + f(2/2) = 7 + 3 + 2 + 1;
f(13/2) + f(6/2) + c(3/2) + f(2/2) + c(1/2) = 6 + 3 + 2 + 1 + 1.

Crossrefs

Sequence in context: A191373 A322873 A332897 * A026904 A057828 A082498

Adjacent sequences: A349549 A349550 A349551 * A349553 A349554 A349555

Keyword

nonn,more

Author

Clark Kimberling, Dec 26 2021

Status

approved