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Number of moved (non-fixed) elements in each permutation given in reversed colexicographic ordering A055089, i.e., the sum of their cycle lengths (excluding the 1-cycles, i.e., fixed elements).
8

%I #25 Jan 22 2024 05:51:35

%S 0,2,2,3,3,2,2,4,3,4,4,3,3,4,2,3,4,4,4,3,3,2,4,4,2,4,4,5,5,4,3,5,4,5,

%T 5,4,4,5,3,4,5,5,5,4,4,3,5,5,3,5,4,5,5,4,2,4,3,4,4,3,4,5,4,5,5,5,5,4,

%U 5,4,5,5,4,5,3,4,5,5,3,4,2,3,4,4,4,5,4,5,5,5,5,5,5,5,4,4,5,4,4,3,5,5,4,3,3

%N Number of moved (non-fixed) elements in each permutation given in reversed colexicographic ordering A055089, i.e., the sum of their cycle lengths (excluding the 1-cycles, i.e., fixed elements).

%C Also number of displacements for permutations in lexicographic order. - _Joerg Arndt_, Jan 22 2024

%H Antti Karttunen, <a href="/A055093/b055093.txt">Table of n, a(n) for n = 0..40320</a>

%H Tilman Piesk, <a href="https://en.wikiversity.org/wiki/Permutations_and_partitions_in_the_OEIS">Permutations and partitions in the OEIS</a> (Wikiversity)

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

%F a(n) = A055090(n) + A055091(n).

%F a(n) = A275812(A290095(n)) = A060129(A060126(n)). - _Antti Karttunen_, Dec 30 2017

%p A055093(n) = count_nonfixed(convert(PermRevLexUnrank(j), 'disjcyc')).

%p count_nonfixed := l -> convert(map(nops,l), `+`);

%p # Procedure PermRevLexUnrank given in A055089.

%Y Cf. A055089, A055090, A055091, A055092, A060129, A275812, A290095.

%K nonn

%O 0,2

%A _Antti Karttunen_, Apr 04 2000

%E Entry revised by _Antti Karttunen_, Dec 30 2017