A369377 a(n) is the number of elements p(j) < j (left displacements) in the n-th permutation in lexicographic order.
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
Keywords
Examples
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
Links
- Joerg Arndt, Table of n, a(n) for n = 0..40319