number of partitions of some k

fn make_next(current: &[u64], i: usize, j: usize) -> Vec<u64> {    let mut new = Vec::with_capacity(current.len()-1);    let add = current[i]+current[j];    //println!("{i},{j}: {}+{}={add}", current[i], current[j]);    for k in 0..current.len() {        let value = if k==i || k==j {0} else {current[k]};        //println!("{k}: {value}");        if value != 0 {            new.push(value);        }    }    let pos = new.binary_search(&add).unwrap_or_else(|e| e);    new.insert(pos, add);    new}fn get_all_next(current: &[u64]) -> Vec<Vec<u64>> {    let mut next: Vec<Vec<u64>> = Vec::new();    for i in 0..current.len() {        for j in i..current.len() {            if i == j { // could maybe replace with just looping j starting from i+1 but wehh                continue;            }            let check = make_next(&current, i, j);            if !(next.contains(&check)) {                next.push(check)            }        }    }    next}fn full_next(last: &[Vec<u64>]) -> Vec<Vec<u64>> {    let mut full_next = Vec::new();    for i in last {        let local_next = get_all_next(&i);        for j in local_next {            if !full_next.contains(&j) {                full_next.push(j);            }        }    }        full_next}fn start(k: u64) -> Vec<u64> {    vec![1u64; k as usize]}fn collect_all(k: u64) -> Vec<Vec<u64>> {    let rounds = (k-2) as usize;    let mut all = Vec::new();    let start = start(k);    let mut next = get_all_next(&start);    all.push(start);    for _ in 0..rounds {        let mut last = next;        next = full_next(last.as_slice());        all.append(&mut last);    }    all}fn main() {    for i in 2..=10 {        let collect = collect_all(i);        println!("{:?}\nLENGTH = {}", collect, collect.len());    }}