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%I #14 Feb 22 2017 15:12:14
%S 1,1,2,4,10,27,79,247,816,2822,10158,37875,145695,576288,2337412,
%T 9698820,41089107,177424188,779699793,3482575169,15791709187,
%U 72621800171,338388714955,1596314968112,7618218238583,36756086159343,179176803145900,882002961543492
%N Number of length n inversion sequences avoiding the patterns 000, 010, 110, and 120.
%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 and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 000, 010, 110, and 120.
%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.
%e For n=3, the inversion sequences are 001, 002, 011, 012.
%e For n=4, the inversion sequences are 0011, 0012, 0013, 0021, 0022, 0023, 0112, 0113, 0122, 0123.
%Y Cf. A263777, A263778, A263779, A263780, A279552, A279553, A279554, A279555, 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 15 2016
%E Typo in comment corrected and a(10)-a(27) added by _Alois P. Heinz_, Feb 22 2017
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