This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279555 #29 Jan 23 2025 03:28:57 %S A279555 1,1,2,5,15,51,189,746,3091,13311,59146,269701,1256820,5966001, %T A279555 28773252,140695923,696332678,3483193924,17589239130,89575160517, %U A279555 459648885327,2374883298183,12346911196912,64555427595970,339276669116222,1791578092326881,9501960180835998 %N A279555 Number of length n inversion sequences avoiding the patterns 110, 210, 120, and 010. %C A279555 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 010, 110, 120, and 210. %C A279555 It can be shown that this sequence also counts the 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, 100, 120, and 210. %C A279555 From _Andrei Asinowski_, Jan 22 2025: (Start) %C A279555 It also enumerates seven other classes of inversion sequences defined by avoidance of four patterns of length 3 (case 166 in Callan and Mansour). %C A279555 It also enumerates inversion sequences that avoid the patterns 011 and 201, and inversion sequences that avoid the patterns 011 and 210. %C A279555 For n >= 1, it also enumerates strong rectangulations that avoid T-shaped joints. (End) %H A279555 Jay Pantone, <a href="/A279555/b279555.txt">Table of n, a(n) for n = 0..500</a> %H A279555 Andrei Asinowski and Michaela A. Polley, <a href="https://arxiv.org/abs/2501.11781">Patterns in rectangulations. Part I: T-like patterns, inversion sequence classes I(010, 101, 120, 201) and I(011, 201), and rushed Dyck paths</a>, arXiv:2501.11781 [math.CO], 2025. %H A279555 David Callan and Toufik Mansour, <a href="https://math.colgate.edu/~integers/x78/x78.pdf">Inversion sequences avoiding quadruple length-3 patterns</a>, Integers, 23 (2023), Article A78. %H A279555 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 A279555 Jay Pantone, <a href="https://doi.org/10.54550/ECA2024V4S4R25">The enumeration of inversion sequences avoiding the patterns 201 and 210</a>, Enumerative Combinatorics and Applications, 4:4 (2024), Article S2R25. %H A279555 Chunyan Yan and Zhicong Lin, <a href="https://arxiv.org/abs/1912.03674">Inversion sequences avoiding pairs of patterns</a>, arXiv:1912.03674 [math.CO], 2019. %F A279555 a(n) ~ c * (1 + sqrt(2))^(2*n) / n^(3/2), where c = 0.00391075995650885016134430802... - _Vaclav Kotesovec_, Jan 23 2025 %e A279555 The length 3 inversion sequences avoiding (010, 110, 120, 210) are 000, 001, 002, 011, 012. %e A279555 The length 4 inversion sequences avoiding (010, 110, 120, 210) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123. %Y A279555 Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573. %K A279555 nonn %O A279555 0,3 %A A279555 _Megan A. Martinez_, Dec 16 2016 %E A279555 a(10)-a(26) from _Alois P. Heinz_, Jan 05 2017