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

Author

Jeffrey Shallit, Sep 16 2019

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A002326, A006694, A081844.

Formula

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