A369376 a(n) is the number of elements p(j) > j (right displacements) in the n-th permutation in lexicographic order.

0, 1, 1, 2, 1, 1, 1, 2, 2, 3, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 3, 3, 2, 3, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 1, 2, 2, 3, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2

Offset

0,4

Links

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

Formula

a(n) + A369377(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 ]   2
   4:    [ . 3 1 2 ]    [ . 2 3 1 ]   1
   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 ]   2
   9:    [ 1 2 3 . ]    [ 3 . 1 2 ]   3
  10:    [ 1 3 . 2 ]    [ 2 . 3 1 ]   2
  11:    [ 1 3 2 . ]    [ 3 . 2 1 ]   2
  12:    [ 2 . 1 3 ]    [ 1 2 . 3 ]   1
  13:    [ 2 . 3 1 ]    [ 1 3 . 2 ]   2
  14:    [ 2 1 . 3 ]    [ 2 1 . 3 ]   1
  15:    [ 2 1 3 . ]    [ 3 1 . 2 ]   2
  16:    [ 2 3 . 1 ]    [ 2 3 . 1 ]   2
  17:    [ 2 3 1 . ]    [ 3 2 . 1 ]   2
  18:    [ 3 . 1 2 ]    [ 1 2 3 . ]   1
  19:    [ 3 . 2 1 ]    [ 1 3 2 . ]   1
  20:    [ 3 1 . 2 ]    [ 2 1 3 . ]   1
  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. A369377, A055093, A034968.

Sequence in context: A029386 A277325 A240837 * A060502 A035439 A059111

Adjacent sequences: A369373 A369374 A369375 * A369377 A369378 A369379

Keyword

nonn

Author

Joerg Arndt, Jan 22 2024

Status

approved