A327551 Number of cycles in the perfect shuffle permutation mapping (1,2,...,2n) to (1,n+1,2,n+2,...,n,2n).

2, 3, 3, 4, 4, 3, 3, 6, 4, 3, 7, 4, 4, 5, 3, 8, 6, 7, 3, 6, 4, 5, 9, 4, 6, 9, 3, 6, 6, 3, 3, 14, 8, 3, 7, 4, 10, 9, 7, 4, 6, 3, 13, 6, 10, 11, 15, 6, 4, 9, 3, 4, 16, 3, 5, 6, 6, 7, 13, 10, 4, 9, 5, 20, 12, 3, 11, 12, 4, 3, 7, 6, 8, 11, 3, 12, 14, 15, 5, 6, 10

Offset

1,1

Comments

The sequence that gives the order of the permutation is A002326.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

Conjecture: a(n) = A006694(n-1) + 2 = A081844(n-1) + 1. - N. J. A. Sloane, Sep 16 2019

Example

For n=4 the permutation is 15263748, which has cycle structure (1)(253)(467)(8).

Maple

f:= proc(n) local p, m; uses GroupTheory;
  p:= Perm([seq(`if`(m::odd, (m+1)/2, n+m/2), m=1..2*n)]);
  nops(PermCycleType(p)) + 2*n - nops(PermSupport(p))
end proc:
map(f, [$1..100]); # Robert Israel, Jul 09 2026

Crossrefs

Cf. A002326, A006694, A081844.

Sequence in context: A366121 A331377 A343754 * A394431 A205324 A359512

Adjacent sequences: A327548 A327549 A327550 * A327552 A327553 A327554

Keyword

nonn,changed

Author

Jeffrey Shallit, Sep 16 2019

Status

approved