A125548 - OEIS

A125548

Number of j-sets in symmetric group S_n.

0, 1, 2, 4, 8, 16, 30, 56, 102, 186, 336, 606, 1088, 1954, 3502, 6278, 11246, 20148, 36086, 64640, 115774, 207374, 371430, 665298, 1191646, 2134454, 3823160, 6847974, 12265912, 21970470, 39353006, 70488334, 126257182, 226149314

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OFFSET

1,3

COMMENTS

For a permutation p=p_1 p_2...p_n in S_n and a positive integer i<= n, we can view p_1 p_2...p_i as an element of S_i by order-preserving relabeling. The j-set of p is the set of i's such that p_1 p_2...p_i is an involution in S_i.

LINKS

Table of n, a(n) for n=1..34.

Christopher Coscia, Jonathan DeWitt, Locally Convex Words and Permutations, Electronic Journal of Combinatorics. 23 (2), 2016, #P2.10.

Dongsu Kim and Jang Soo Kim, The Initial Involution Patterns of Permutations, Electron. J. Combin., Vol. 14 (1) (2007), #R2.

FORMULA

Kim and Kim give a g.f.

CROSSREFS

Sequence in context: A075529 A005305 A298402 * A227298 A164229 A054668

Adjacent sequences: A125545 A125546 A125547 * A125549 A125550 A125551

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 03 2007

EXTENSIONS

More terms from Vladeta Jovovic, Jan 03 2007

STATUS

approved