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

Author

Pontus von Brömssen, Mar 05 2023

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

First column of A361221.

Cf. A102462.