A361223 - OEIS

A361223

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

%I #9 Mar 11 2023 09:39:29

%S 1,1,1,2,2,4,6,10,16,30,54,84,140,252,420,756,1260,2520,4620,7920,

%T 13860,27720,51480,90120,180180,337890,600600,1081080,2042040,3675672,

%U 6348888,12252240,23279256,42325920,77597520,148140720,271591320,480507720,892371480

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

%H Pontus von Brömssen, <a href="/A361223/b361223.txt">Table of n, a(n) for n = 1..100</a>

%e For n = 5, the 7 partitions have the following permutations (~ means equivalence under reversal):

%e permutations | number of inequivalent permutations

%e ---------------------+------------------------------------

%e 5 | 1

%e 41~14 | 1

%e 32~23 | 1

%e 311~113, 131 | 2

%e 221~122, 212 | 2

%e 2111~1112, 1211~1121 | 2

%e 11111 | 1

%e The maximum number of inequivalent permutations is 2 (for the partitions 311, 221, and 2111), so a(5) = 2.

%Y First column of A361221.

%Y Cf. A102462.

%K nonn

%O 1,4

%A _Pontus von Brömssen_, Mar 05 2023