A380576 Total number of "block reversals" needed to transform all permutations of [n] into 12...n.

0, 0, 1, 7, 42, 287, 2186, 18650, 176408, 1837189, 20908724, 258210463, 3440203098, 49202385314, 752012692572

Offset

0,4

Links

Table of n, a(n) for n=0..14.

Wikipedia, Permutation

Formula

a(n) = Sum_{k>=1} k * A300003(n,k).

Example

a(3) = 7:
  123,
  1(32) -> 123,
  (21)3 -> 123,
  (23)1 -> (321) -> 123,
  3(12) -> (321) -> 123,
  (321) -> 123.

Crossrefs

Cf. A300003.

Sequence in context: A187246 A278152 A366222 * A332082 A271427 A073506

Adjacent sequences: A380573 A380574 A380575 * A380577 A380578 A380579

Keyword

nonn,more

Author

Alois P. Heinz, Mar 26 2025

Extensions

a(13)-a(14) from Bert Dobbelaere, Apr 12 2025

Status

approved