%I #26 Jul 12 2024 09:51:58
%S 1,1,2,6,22,87,354,1465,6154,26223,113236,494870,2185700,9743281,
%T 43784838,198156234,902374498,4131895035,19012201080,87864535600,
%U 407664831856,1898184887679,8867042353912,41543375724751,195164372948152,919138464708907,4338701289961694,20524046955770940
%N Number of length n inversion sequences avoiding the patterns 102 and 201.
%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 102 and 201.
%H Benjamin Testart, <a href="/A279566/b279566.txt">Table of n, a(n) for n = 0..1400</a>
%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], 2016-2018.
%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.
%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.
%F G.f.: (-8*x^4 + 18*x^3 - 10*x^2 - 8*x + 4 + 2 * (2*x - 1) * (x^2 - 2*x + 2) * ((5*x - 1)*(x - 1))^(1/2)) / (4*x * (2*x - 1) * (x - 1) * (x - 2)^2). - _Benjamin Testart_, Jul 12 2024
%e The length 4 inversion sequences avoiding (102, 201) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0110, 0111, 0112, 0113, 0120, 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, A279567, A279568, A279569, A279570, A279571, A279572, A279573.
%K nonn
%O 0,3
%A _Megan A. Martinez_, Feb 09 2017
%E a(10)-a(11) from _Alois P. Heinz_, Feb 24 2017
%E a(12)-a(17) from _Bert Dobbelaere_, Dec 30 2018
%E a(18) and beyond from _Benjamin Testart_, Jul 12 2024