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
Examples
a(3) = 6 because all six permutations in S_3 have this property.
Links
- S. Fishel, E. Milicevic, R. Patrias, and B. E. Tenner, Enumerations relating braid and commutation classes, arXiv:1708.04372 [math.CO], 2017.
Programs
-
Magma
[1] cat [Catalan(n) + n - 2: n in [2..40]]; // Vincenzo Librandi, Aug 16 2017
-
Mathematica
Join[{1}, Table[CatalanNumber[n] + n - 2, {n, 2, 30}]] (* Vincenzo Librandi, Aug 16 2017 *)
Formula
a(1) = 1 and a(n) = C(n) + n - 2 for n > 1, where C(n) is the n-th Catalan number.