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A369377
a(n) is the number of elements p(j) < j (left displacements) in the n-th permutation in lexicographic order.
2
0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 3, 2, 2, 1, 2, 2, 1, 2, 2, 2, 3, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 3, 2, 2, 1, 2, 2, 2, 3, 2, 2, 3, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 4, 3, 3, 2, 3, 3, 3, 2, 2, 1, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 3, 2, 2
OFFSET
0,5
FORMULA
a(n) + A369376(n) = A055093(n).
EXAMPLE
In the following dots are used for zeros in the permutations and their inverses.
n: permutation inv. perm. a(n)
0: [ . 1 2 3 ] [ . 1 2 3 ] 0
1: [ . 1 3 2 ] [ . 1 3 2 ] 1
2: [ . 2 1 3 ] [ . 2 1 3 ] 1
3: [ . 2 3 1 ] [ . 3 1 2 ] 1
4: [ . 3 1 2 ] [ . 2 3 1 ] 2
5: [ . 3 2 1 ] [ . 3 2 1 ] 1
6: [ 1 . 2 3 ] [ 1 . 2 3 ] 1
7: [ 1 . 3 2 ] [ 1 . 3 2 ] 2
8: [ 1 2 . 3 ] [ 2 . 1 3 ] 1
9: [ 1 2 3 . ] [ 3 . 1 2 ] 1
10: [ 1 3 . 2 ] [ 2 . 3 1 ] 2
11: [ 1 3 2 . ] [ 3 . 2 1 ] 1
12: [ 2 . 1 3 ] [ 1 2 . 3 ] 2
13: [ 2 . 3 1 ] [ 1 3 . 2 ] 2
14: [ 2 1 . 3 ] [ 2 1 . 3 ] 1
15: [ 2 1 3 . ] [ 3 1 . 2 ] 1
16: [ 2 3 . 1 ] [ 2 3 . 1 ] 2
17: [ 2 3 1 . ] [ 3 2 . 1 ] 2
18: [ 3 . 1 2 ] [ 1 2 3 . ] 3
19: [ 3 . 2 1 ] [ 1 3 2 . ] 2
20: [ 3 1 . 2 ] [ 2 1 3 . ] 2
21: [ 3 1 2 . ] [ 3 1 2 . ] 1
22: [ 3 2 . 1 ] [ 2 3 1 . ] 2
23: [ 3 2 1 . ] [ 3 2 1 . ] 2
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jan 22 2024
STATUS
approved