OFFSET
1,2
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 = 2, 3, ..., k.
EXAMPLE
Let f = floor and c = ceiling.
a(1) = 0 corresponds to the empty halving partition of 0.
a(3) = 5, since 5 is the smallest number with 3 halving partitions:
c(5/2) + c(3/2) = 5;
c(5/2) + f(3/2) + c(1/2) = 3 + 1 + 1 = 5;
f(5/2) + (2/2) + c(1/2) + c(1/2) = 2 + 1 + 1 + 1.
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 26 2021
EXTENSIONS
Corrected and extended by Max Alekseyev, Sep 30 2024
STATUS
approved