A279570 - OEIS

%I #16 Jul 12 2024 07:52:10

%S 1,1,2,6,22,92,423,2091,10950,60120,343453,2029809,12354661,77168197,

%T 493189283,3217459119,21382723456,144518555231,991885282987,

%U 6904454991721,48691257834999,347542736059492,2508603139285095,18297609829743478,134772911886028731

%N Number of length n inversion sequences avoiding the patterns 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 > e_k and e_i > e_k. This is the same as the set of length n inversion sequences avoiding 110 and 120.

%H Benjamin Testart, <a href="/A279570/b279570.txt">Table of n, a(n) for n = 0..350</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/2407.07701">Completing the enumeration of inversion sequences avoiding one or two patterns of length 3</a>, arXiv:2407.07701 [math.CO], 2024.

%e The length 4 inversion sequences avoiding (110,120) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0102, 0103, 0111, 0112, 0113, 0121, 0122, 0123.

%Y Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279571, A279572, A279573.

%K nonn

%O 0,3

%A _Megan A. Martinez_, Feb 21 2017

%E a(10)-a(24) from _Alois P. Heinz_, Feb 21 2017