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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.

%I A290954 #8 Aug 16 2017 08:43:59
%S A290954 1,2,6,23,65,177,506,1551,5041,17049,59131,208469,743491,2675189,
%T A290954 9695778,35358815,129646177,477640361,1767265159,6564122733,
%U A290954 24466269715,91482566757,343059617231,1289904151413,4861946406095,18367353077397,69533550921901,263747951756961,1002242216658727,3814986502100477
%N 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.
%H A290954 S. Fishel, E. Milicevic, R. Patrias, and B. E. Tenner, <a href="https://arxiv.org/abs/1708.04372">Enumerations relating braid and commutation classes</a>, arXiv:1708.04372 [math.CO], 2017.
%F A290954 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.
%e A290954 a(3) = 6 because all six permutations in S_3 have this property.
%Y A290954 Cf. A000108, A290953.
%K A290954 easy,nonn
%O A290954 1,2
%A A290954 _Bridget Tenner_, Aug 15 2017