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 A368500 #15 Jan 01 2024 09:12:35 %S A368500 1,0,2,0,2,4,0,2,20,2,0,2,76,42,0,2,252,466,0,2,788,4110,140,0,2,2374, %T A368500 32388,5556,0,2,6938,236966,118974,0,2,19778,1652490,1952530,4000,0,2, %U A368500 55222,11173264,28078784,609528,0,2,151462,74003396,370327224,34519516 %N A368500 Table read by rows: T(n, k) is the number of permutations of size n whose incidence graph has treewidth k. %C A368500 The incidence graph of a permutation p is the union of the two path graphs 1 - 2 - ... - n and p(1) - p(2) - ... - p(n). %C A368500 Column k = 0 is all zeros except for n = 1. Column k = 1 is all twos because the only permutations that have an incidence graph with no cycles are the identity permutation and its reverse. %H A368500 S. Ahal and Y. Rabinovich, <a href="https://doi.org/10.1137/S0895480104444776">On complexity of the subpattern problem</a>, SIAM J. Discrete Math., Vol. 22, No. 2 (2008), pp. 629-649. %H A368500 Wikipedia, <a href="https://en.wikipedia.org/wiki/Treewidth">Treewidth</a> %e A368500 T(4, 3) is 2 because there are two permutations of size 4 with an incidence graph of treewidth 3. Namely, (2,4,1,3) and (3,1,4,2): these have K_4 as their incidence graphs. %e A368500 Table begins at row n = 1 and column k = 0 as: %e A368500 1; %e A368500 0, 2; %e A368500 0, 2, 4; %e A368500 0, 2, 20, 2; %e A368500 0, 2, 76, 42; %e A368500 0, 2, 252, 466; %e A368500 0, 2, 788, 4110, 140; %e A368500 0, 2, 2374, 32388, 5556; %e A368500 0, 2, 6938, 236966, 118974; %e A368500 0, 2, 19778, 1652490, 1952530, 4000; %e A368500 0, 2, 55222, 11173264, 28078784, 609528; %e A368500 0, 2, 151462, 74003396, 370327224, 34519516; %e A368500 ... %Y A368500 Row sums give A000142. %K A368500 nonn,tabf %O A368500 1,3 %A A368500 _Martín Muñoz_, Dec 27 2023