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

1,7

Links

Table of n, a(n) for n=1..55.

Prog

(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)

Crossrefs

Cf. A000005, A239497, A386361.

Cf. A237825.

Sequence in context: A123015 A005434 A027589 * A039851 A239100 A337046

Adjacent sequences: A386357 A386358 A386359 * A386361 A386362 A386363

Keyword

nonn

Author

Seiichi Manyama, Jul 19 2025

Status

approved