OFFSET
1,2
COMMENTS
For n not equal to 2, a(n) is the minimal sum of squares over balanced partitions of n.
a(n) is strictly increasing and has parity equal to n.
LINKS
Sela Fried, Table of n, a(n) for n = 1..1000
Sela Fried, The minimal sum of squares over partitions with a nonnegative rank, Annals of Combinatorics, 2022.
FORMULA
a(n) = Theta(n^(4/3)).
EXAMPLE
Both (5, 3, 3, 3, 3) and (6, 3, 2, 2, 2, 2) are balanced and have the minimal sum of squares of 61 over balanced partitions of n = 17.
PROG
(PARI) a(n) = my(m=oo); forpart(p=n, if (vecmax(p) >= #p, m = min(m, norml2(Vec(p)))); ); m; \\ Michel Marcus, Aug 09 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Sela Fried, Apr 19 2022
STATUS
approved