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

0,5

Links

Joerg Arndt, Table of n, a(n) for n = 0..40319

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

Cf. A369376, A055093, A034968.

Sequence in context: A322811 A091853 A193773 * A091304 A340101 A049847

Adjacent sequences: A369374 A369375 A369376 * A369378 A369379 A369380

Keyword

nonn

Author

Joerg Arndt, Jan 22 2024

Status

approved