The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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, arXiv:2204.07873 [math.CO], 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 Cf. A064174, A047993. Sequence in context: A047376 A260989 A285566 * A293790 A190778 A117573 Adjacent sequences:  A353041 A353042 A353043 * A353045 A353046 A353047 KEYWORD nonn,changed AUTHOR Sela Fried, Apr 19 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 16 21:38 EDT 2022. Contains 356169 sequences. (Running on oeis4.)