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

Author

Joerg Arndt, Jan 22 2024

Keywords

• nonn

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

Crossrefs

Cf. A369376, A055093, A034968.

Formula

a(n) + A369376(n) = A055093(n).