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

%I A361223 #9 Mar 11 2023 09:39:29
%S A361223 1,1,1,2,2,4,6,10,16,30,54,84,140,252,420,756,1260,2520,4620,7920,
%T A361223 13860,27720,51480,90120,180180,337890,600600,1081080,2042040,3675672,
%U A361223 6348888,12252240,23279256,42325920,77597520,148140720,271591320,480507720,892371480
%N A361223 Maximum number of inequivalent permutations of a partition of n, where two permutations are equivalent if they are reversals of each other.
%H A361223 Pontus von Brömssen, <a href="/A361223/b361223.txt">Table of n, a(n) for n = 1..100</a>
%e A361223 For n = 5, the 7 partitions have the following permutations (~ means equivalence under reversal):
%e A361223   permutations         | number of inequivalent permutations
%e A361223   ---------------------+------------------------------------
%e A361223           5            |   1
%e A361223         41~14          |   1
%e A361223         32~23          |   1
%e A361223     311~113, 131       |   2
%e A361223     221~122, 212       |   2
%e A361223   2111~1112, 1211~1121 |   2
%e A361223         11111          |   1
%e A361223 The maximum number of inequivalent permutations is 2 (for the partitions 311, 221, and 2111), so a(5) = 2.
%Y A361223 First column of A361221.
%Y A361223 Cf. A102462.
%K A361223 nonn
%O A361223 1,4
%A A361223 _Pontus von Brömssen_, Mar 05 2023