cp's OEIS Frontend

A279556 Number of length n inversion sequences avoiding the patterns 010, 110, and 120.

%I A279556 #29 Sep 02 2025 21:56:16
%S A279556 1,1,2,5,15,51,190,759,3206,14180,65203,309998,1517330,7619541,
%T A279556 39145113,205261890,1096393056,5955598301,32852080738,183797522935,
%U A279556 1041802426740,5977047039743,34679912608313,203345277644481,1204104271508239,7196256426157901
%N A279556 Number of length n inversion sequences avoiding the patterns 010, 110, and 120.
%C A279556 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, 110, and 120.
%H A279556 Nicholas R. Beaton, <a href="/A279556/b279556.txt">Table of n, a(n) for n = 0..54</a>
%H A279556 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], 2016-2018.
%e A279556 The length 3 inversion sequences avoiding (010, 110, 120) are 000, 001, 002, 011, 012
%e A279556 The length 4 inversion sequences avoiding (010, 110, 120) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.
%Y A279556 Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.
%K A279556 nonn,changed
%O A279556 0,3
%A A279556 _Megan A. Martinez_, Dec 16 2016
%E A279556 a(10)-a(11) from _Alois P. Heinz_, Feb 24 2017
%E A279556 a(12)-a(16) from _Bert Dobbelaere_, Dec 30 2018
%E A279556 a(17)-a(25) from _Nicholas R. Beaton_, Aug 29 2025