A361223 Maximum number of inequivalent permutations of a partition of n, where two permutations are equivalent if they are reversals of each other.

1, 1, 1, 2, 2, 4, 6, 10, 16, 30, 54, 84, 140, 252, 420, 756, 1260, 2520, 4620, 7920, 13860, 27720, 51480, 90120, 180180, 337890, 600600, 1081080, 2042040, 3675672, 6348888, 12252240, 23279256, 42325920, 77597520, 148140720, 271591320, 480507720, 892371480

Offset

1,4

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..100

Example

For n = 5, the 7 partitions have the following permutations (~ means equivalence under reversal):
  permutations         | number of inequivalent permutations
  ---------------------+------------------------------------
          5            |   1
        41~14          |   1
        32~23          |   1
    311~113, 131       |   2
    221~122, 212       |   2
  2111~1112, 1211~1121 |   2
        11111          |   1
The maximum number of inequivalent permutations is 2 (for the partitions 311, 221, and 2111), so a(5) = 2.

Crossrefs

First column of A361221.

Cf. A102462.

Sequence in context: A300865 A053637 A000016 * A060553 A293673 A344707

Adjacent sequences: A361220 A361221 A361222 * A361224 A361225 A361226

Keyword

nonn

Author

Pontus von Brömssen, Mar 05 2023

Status

approved