A386361 Number of partitions of n such that the least part occurs exactly (1/4)*(number of parts) times.

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 9, 12, 16, 20, 26, 32, 41, 50, 62, 76, 93, 112, 136, 164, 197, 237, 283, 339, 403, 480, 569, 676, 799, 945, 1113, 1314, 1543, 1815, 2125, 2494, 2912, 3407, 3970, 4632, 5384, 6266, 7268, 8438, 9766, 11310, 13063, 15097, 17402

Offset

1,9

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 A386361(n)
  (1..n).map{|i| A(i, 4)}
end
p A386361(40)

Crossrefs

Cf. A000005, A239497, A386360.

Cf. A237826.

Sequence in context: A026317 A361848 A008768 * A067593 A084993 A046966

Adjacent sequences: A386358 A386359 A386360 * A386362 A386363 A386364

Keyword

nonn

Author

Seiichi Manyama, Jul 19 2025

Status

approved