|
%I #20 Feb 01 2023 07:09:54
%S 1,1,2,5,15,52,201,845,3801,18089,90316,470010,2536077,14127741,
%T 80966690,475979359,2863157581,17585971037,110095460224,701418693025,
%U 4541497543092,29847982448766,198913925919741,1342890255133042,9176456969273844,63422002415068463
%N Number of length n inversion sequences avoiding the patterns 010 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 010 and 120.
%H Benjamin Testart, <a href="/A279559/b279559.txt">Table of n, a(n) for n = 0..400</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 Benjamin Testart, <a href="https://arxiv.org/abs/2212.07222">Inversion sequences avoiding the pattern 010</a>, arXiv:2212.07222 [math.CO], 2022.
%H Chunyan Yan, 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 4 inversion sequences avoiding (010, 120) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.
%Y Cf. A000108, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.
%K nonn
%O 0,3
%A _Megan A. Martinez_, Jan 17 2017
%E a(10)-a(25) from _Alois P. Heinz_, Feb 22 2017
|
