|
%I #17 Feb 01 2023 07:09:22
%S 1,1,2,4,10,29,95,345,1376,5966,27886,139608,744552,4210191,25140790,
%T 157981820,1041480482,7183374125,51711299169,387683162541,
%U 3020997261596,24424884853963,204559337781097,1772011400733378,15855597322378302,146360032952969570
%N Number of length n inversion sequences avoiding the patterns 000 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 000 and 010.
%H Benjamin Testart, <a href="/A279552/b279552.txt">Table of n, a(n) for n = 0..200</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.
%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, A279551, 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 a(10)-a(20) from _Alois P. Heinz_, Feb 23 2017
%E a(21) onwards from _Benjamin Testart_, Feb 01 2023
|
