A378834 Number of ways to reverse a permutation of n elements by the minimum number of steps of rotate left or right 1 place (L,R), or exchange first two elements (E).

1, 3, 2, 2, 2, 6, 6, 32, 32, 240, 240, 2304, 2304

Offset

1,2

Comments

The minimum number of steps is A186752(n).

For n=2, steps L,R,E all have the same effect but each is taken as a separate way so that a(2) = 3.

For 4 <= n <= 13, a(n) = (h+2)*2^h*h! where h = floor((n-4)/2).

Links

Table of n, a(n) for n=1..13.

Example

For n=1, permutation {1} is already its own reversal so has a(1) = 1 way of no steps (A186752(1) = 0).
For n=5, the a(5) = 2 ways to reverse {1,2,3,4,5} by A186752(5) = 8 steps are
  E, L, L, E, L, E, R, E
  E, L, E, R, E, R, R, E
Notice these are inverses: reverse the order and flip L<->R in one makes the other.

Crossrefs

Cf. A186752 (number of steps).

Cf. A061545 (ways for LE).

Sequence in context: A134653 A377320 A090207 * A364571 A202538 A239736

Adjacent sequences: A378831 A378832 A378833 * A378835 A378836 A378837

Keyword

nonn,more

Author

Kevin Ryde, Dec 09 2024

Status

approved