A290954 The number of permutations in S_n for which the number of reduced words is minimized with respect to the numbers of braid and commutation classes: |R(w)| = |B(w)| + |C(w)| - 1.
1, 2, 6, 23, 65, 177, 506, 1551, 5041, 17049, 59131, 208469, 743491, 2675189, 9695778, 35358815, 129646177, 477640361, 1767265159, 6564122733, 24466269715, 91482566757, 343059617231, 1289904151413, 4861946406095, 18367353077397, 69533550921901, 263747951756961, 1002242216658727, 3814986502100477
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.
Formula
a(1) = 1, a(2) = 2, and a(n) = C(n) + (n^3 - 3n^2 + 8n - 21)/3 for n > 2, where C(n) is the n-th Catalan number.