login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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
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
Sequence in context: A378341 A337318 A333070 * A151391 A166896 A148440
KEYWORD
easy,nonn
AUTHOR
Bridget Tenner, Aug 15 2017
STATUS
approved