A386360 Number of partitions of n such that the least part occurs exactly (1/3)*(number of parts) times.

0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 8, 10, 13, 17, 21, 27, 33, 41, 50, 63, 75, 93, 111, 136, 163, 198, 235, 285, 337, 406, 479, 574, 676, 806, 948, 1124, 1318, 1557, 1822, 2147, 2505, 2940, 3424, 4006, 4657, 5431, 6299, 7329, 8483, 9843, 11372, 13163, 15177, 17527, 20175

Offset: 1

Author

Seiichi Manyama, Jul 19 2025

Keywords

• nonn

Crossrefs

Cf. A000005, A239497, A386361.

Cf. A237825.

Programs

Ruby

def partition(n, min, max)
  return [[]] if n == 0
  [max, n].min.downto(min).flat_map{|i| partition(n - i, min, i).map{|rest| [i, *rest]}}
end
def A(n, k)
  cnt = 0
  partition(n, 1, n).each{|ary|
    cnt += 1 if k * ary.count(ary.min) == ary.size
  }
  cnt
end
def A386360(n)
  (1..n).map{|i| A(i, 3)}
end
p A386360(40)