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 A360196 #15 Feb 16 2025 08:34:04 %S A360196 1,2,2,3,5,3,4,9,9,4,5,14,24,14,5,6,20,58,58,20,6,7,27,125,229,125,27, %T A360196 7,8,35,251,749,749,251,35,8,9,44,490,2180,3436,2180,490,44,9,10,54, %U A360196 948,6188,13350,13350,6188,948,54,10,11,65,1823,17912,50203,65772,50203,17912,1823,65,11 %N A360196 Array read by antidiagonals: T(m,n) is the number of induced cycles in the grid graph P_m X P_n. %C A360196 Induced cycles are sometimes called chordless cycles (but some definitions require chordless cycles to have a cycle length of at least 4). %H A360196 Andrew Howroyd, <a href="/A360196/b360196.txt">Table of n, a(n) for n = 2..497</a> %H A360196 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChordlessCycle.html">Chordless Cycle</a>. %H A360196 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>. %H A360196 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cycle_(graph_theory)">Cycle (graph theory)</a>. %F A360196 T(m,n) = T(n,m). %e A360196 Array begins: %e A360196 ======================================================== %e A360196 m\n| 2 3 4 5 6 7 8 9 ... %e A360196 ---+---------------------------------------------------- %e A360196 2 | 1 2 3 4 5 6 7 8 ... %e A360196 3 | 2 5 9 14 20 27 35 44 ... %e A360196 4 | 3 9 24 58 125 251 490 948 ... %e A360196 5 | 4 14 58 229 749 2180 6188 17912 ... %e A360196 6 | 5 20 125 749 3436 13350 50203 196918 ... %e A360196 7 | 6 27 251 2180 13350 65772 308212 1535427 ... %e A360196 8 | 7 35 490 6188 50203 308212 1743247 10614143 ... %e A360196 9 | 8 44 948 17912 196918 1535427 10614143 78586742 ... %e A360196 ... %Y A360196 Main diagonal is A297664. %Y A360196 Rows 2..5 are A000027(n-1), A000096(n-1), A360197, A360198. %Y A360196 Cf. A231829 (undirected cycles), A287151 (connected induced subgraphs), A360199 (induced paths), A360202 (induced trees), A360913 (maximum induced cycles). %K A360196 nonn,tabl %O A360196 2,2 %A A360196 _Andrew Howroyd_, Jan 29 2023