A055093 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).

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, 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, 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

Offset

0,2

Comments

Also number of displacements for permutations in lexicographic order. - Joerg Arndt, Jan 22 2024

Links

Antti Karttunen, Table of n, a(n) for n = 0..40320

Tilman Piesk, Permutations and partitions in the OEIS (Wikiversity)

Index entries for sequences related to factorial base representation

Formula

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

a(n) = A275812(A290095(n)) = A060129(A060126(n)). - Antti Karttunen, Dec 30 2017

Maple

A055093(n) = count_nonfixed(convert(PermRevLexUnrank(j), 'disjcyc')).
count_nonfixed := l -> convert(map(nops, l), `+`);
# Procedure PermRevLexUnrank given in A055089.

Crossrefs

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

Sequence in context: A340327 A332249 A049113 * A196058 A081844 A233549

Adjacent sequences: A055090 A055091 A055092 * A055094 A055095 A055096

Keyword

nonn

Author

Antti Karttunen, Apr 04 2000

Extensions

Entry revised by Antti Karttunen, Dec 30 2017

Status

approved