A007974 Number of permutations that are n-3 "block reversals" away from 12...n.

1, 6, 52, 389, 2539, 16604, 105365, 654030, 3900116, 22073230, 116855950, 567965207

Offset: 3

Author

J. H. Conway

Keywords

• nonn
• more

Crossrefs

Cf. A007972, A007973, A007975, A300003.

Programs

Python

def a(n):
    perm = tuple(range(1, n+1)); reach = {perm}; frontier = {perm}
    for k in range(n-3):
        r1 = set()
        while len(frontier) > 0:
            q = frontier.pop()
            for i in range(n):
                for j in range(i+1, n+1):
                    qp = list(q)
                    qp[i:j] = qp[i:j][::-1]
                    qp = tuple(qp)
                    if qp not in reach:
                        reach.add(qp)
                        r1.add(qp)
        frontier = r1
    return len(frontier)
print([a(n) for n in range(3, 10)]) # Michael S. Branicky, Jan 26 2023

Formula

a(n) = A300003(n,n-3).

Extensions

a(9)-a(11) from Sean A. Irvine, Feb 22 2018

a(12) from Thomas Baruchel, Mar 26 2025

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