%I #18 Dec 31 2018 06:16:57

%S 1,1,2,5,15,51,188,733,2979,12495,53708,235396,1048168,4728757,

%T 21569339,99309057,460932778,2154402107

%N Number of length n inversion sequences avoiding the patterns 010, 101, 120, 201, and 210.

%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_i <> e_j <> e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 101, 120, 201, and 210.

%H Megan A. Martinez, 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], 2016-2018.

%e The length 3 inversion sequences are 000, 001, 002, 011, 012.

%e The length 4 inversion sequences 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, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

%K nonn,more

%O 0,3

%A _Megan A. Martinez_, Dec 15 2016

%E a(10)-a(11) from _Alois P. Heinz_, Feb 24 2017

%E a(12)-a(17) from _Bert Dobbelaere_, Dec 30 2018