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 A346624 #24 Jul 09 2025 04:56:23 %S A346624 1,1,1,1,1,1,1,1,3,3,3,2,1,1,3,38,242,1100,3441,8438,15392,19002, %T A346624 16293,10624,5857,3044,1546,786,393,198,105,55,28,14,8,4,2,1 %N A346624 Irregular triangle read by rows: T(n,k) is the number of distinct Wilf classes of subsets of exactly k patterns in S_n, for 0 <= k <= n!. %C A346624 For T(4,1) and T(4,2) see the references in the Callan et el. articles. %D A346624 T. Mansour and M. Schork, Wilf classification of subsets of four letter patterns, Journal of Combinatorics and Number Theory 8:1 (2016) 1--111. %D A346624 T. Mansour and M. Schork, Wilf classification of subsets of eight and nine four-letter patterns, Journal of Combinatorics and Number Theory 8:3 (2016) 27pp. %D A346624 T. Mansour and M. Schork, Wilf classification of subsets of six and seven four-letter patterns, Journal of Combinatorics and Number Theory 9:3 (2017). %H A346624 D. Callan, T. Mansour and M. Shattuck, <a href="https://doi.org/10.23638/DMTCS-19-1-5">Wilf classification of triples of 4-letter patterns I</a>, Discrete Mathematics & Theoretical Computer Science 19:1 (2017) #5. %H A346624 D. Callan, T. Mansour and M. Shattuck, <a href="https://doi.org/10.23638/DMTCS-19-1-6">Wilf classification of triples of 4-letter patterns II</a>, Discrete Mathematics & Theoretical Computer Science 19:1 (2017) #6. %H A346624 D. Callan, T. Mansour and M. Shattuck, <a href="https://doi.org/10.1515/puma-2015-0031">Enumeration of permutations avoiding a triple of 4-letter patterns is almost all done</a>, Pure Mathematics and Applications 28:1 (2019) 14--69. %H A346624 T. Mansour, <a href="https://doi.org/10.47443/cm.2020.0006">Enumeration and Wilf-classification of permutations avoiding five patterns of length 4</a>, Contributions to Mathematics 1 (2020) 1--10. %H A346624 T. Mansour, <a href="https://www.dmlett.com/archive/DML20_v3_p67_94.pdf">Enumeration and Wilf-classification of permutations avoiding four patterns of length 4</a>, Discrete Mathematics Letters 3 (2020) 67--94. %H A346624 Toufik Mansour, <a href="https://sites.math.rutgers.edu/~zeilberg/ardz/ToufikMansour.pdf">Restricted Permutations, Conjecture of Lin and Kim, and Work of Andrews and Chern</a>, Talk presented at Workshop "Combinatorics and Algebras from Amitai Regev to Doron Zeilberger", July 26-29, 2021. %H A346624 Rodica Simion and Frank W. Schmidt, <a href="https://doi.org/10.1016/S0195-6698(85)80052-4">Restricted Permutations</a>, Europ. J. Combinatorics, 6 (1985), 383-406. %e A346624 The rows corresponding to S_0, S_1, S_2, S_3, and S_4 are: %e A346624 1, %e A346624 1, 1, %e A346624 1, 1, 1, %e A346624 1, 1, 3, 3, 3, 2, 1, %e A346624 1, 3, 38, 242, 1100, 3441, 8438, 15392, 19002, 16293, 10624, 5857, 3044, 1546, 786, 393, 198, 105, 55, 28, 14, 8, 4, 2, 1. %Y A346624 Cf. A099952. %K A346624 nonn,tabf,more %O A346624 0,9 %A A346624 _N. J. A. Sloane_, Jul 28 2021, based on information supplied by Toufik Mansour