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Number of length n inversion sequences avoiding the patterns 110, 210, 120, and 010.
27

%I #18 Oct 11 2023 15:19:39

%S 1,1,2,5,15,51,189,746,3091,13311,59146,269701,1256820,5966001,

%T 28773252,140695923,696332678,3483193924,17589239130,89575160517,

%U 459648885327,2374883298183,12346911196912,64555427595970,339276669116222,1791578092326881,9501960180835998

%N Number of length n inversion sequences avoiding the patterns 110, 210, 120, and 010.

%C A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i<j<k) such that e_j > e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 110, 120, and 210.

%C It can be shown that this sequence also counts the length n inversion sequences with no entries e_i, e_j, e_k (where i<j<k) such that e_i <> e_j >=e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 100, 120, and 210.

%H Jay Pantone, <a href="/A279555/b279555.txt">Table of n, a(n) for n = 0..500</a>

%H Megan A. Martinez and Carla D. Savage, <a href="https://arxiv.org/abs/1609.08106">Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations</a>, arXiv:1609.08106 [math.CO], 2016.

%H Chunyan Yan and Zhicong Lin, <a href="https://arxiv.org/abs/1912.03674">Inversion sequences avoiding pairs of patterns</a>, arXiv:1912.03674 [math.CO], 2019.

%e The length 3 inversion sequences avoiding (010, 110, 120, 210) are 000, 001, 002, 011, 012.

%e The length 4 inversion sequences avoiding (010, 110, 120, 210) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

%Y Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

%K nonn

%O 0,3

%A _Megan A. Martinez_, Dec 16 2016

%E a(10)-a(26) from _Alois P. Heinz_, Jan 05 2017