A290953 The number of permutations in S_n for which the number of reduced words is maximized with respect to the numbers of braid and commutation classes: |R(w)| = |B(w)| * |C(w)|.

1, 2, 6, 16, 45, 136, 434, 1436, 4869, 16804, 58795, 208022, 742911, 2674452, 9694858, 35357684, 129644805, 477638716, 1767263207, 6564120438, 24466267039, 91482563660, 343059613671, 1289904147346, 4861946401475, 18367353072176, 69533550916029, 263747951750386, 1002242216651395, 3814986502092332

Offset

1,2

Links

Table of n, a(n) for n=1..30.

S. Fishel, E. Milicevic, R. Patrias, and B. E. Tenner, Enumerations relating braid and commutation classes, arXiv:1708.04372 [math.CO], 2017.

Formula

a(1) = 1 and a(n) = C(n) + n - 2 for n > 1, where C(n) is the n-th Catalan number.

Example

a(3) = 6 because all six permutations in S_3 have this property.

Mathematica

Join[{1}, Table[CatalanNumber[n] + n - 2, {n, 2, 30}]] (* Vincenzo Librandi, Aug 16 2017 *)

Prog

(Magma) [1] cat [Catalan(n) + n - 2: n in [2..40]]; // Vincenzo Librandi, Aug 16 2017

Crossrefs

Cf. A000108, A290954.

Sequence in context: A378341 A337318 A333070 * A151391 A166896 A148440

Adjacent sequences: A290950 A290951 A290952 * A290954 A290955 A290956

Keyword

easy,nonn

Author

Bridget Tenner, Aug 15 2017

Status

approved