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A353044
a(n) is the minimal sum of squares over partitions of n with a nonnegative rank.
1
1, 4, 5, 8, 11, 14, 17, 22, 25, 28, 33, 38, 41, 46, 51, 56, 61, 66, 71, 76, 81, 88, 93, 98, 103, 110, 117, 122, 127, 134, 141, 148, 153, 160, 167, 174, 181, 188, 195, 202, 209, 216, 223, 230, 237, 244, 253, 260, 267, 274, 281, 290, 299
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.
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
Sequence in context: A047376 A260989 A285566 * A293790 A190778 A117573
KEYWORD
nonn
AUTHOR
Sela Fried, Apr 19 2022
STATUS
approved