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 A360854 #8 Feb 16 2025 08:34:04
%S A360854 0,1,21,236,4040,114105,4662721,256485936,18226110456,1623855703785,
%T A360854 177195820502965,23237493232958796,3605437233380103056,
%U A360854 653193551573628910481,136634950180317224879985,32681589590709963123110080,8863149183726257535369656976
%N A360854 Number of induced cycles in the n X n rook graph.
%C A360854 Induced cycles are sometimes called chordless cycles (but some definitions require chordless cycles to have a cycle length of at least 4). See A070968 for the version that excludes triangles.
%H A360854 Andrew Howroyd, <a href="/A360854/b360854.txt">Table of n, a(n) for n = 1..100</a>
%H A360854 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>.
%H A360854 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cycle_(graph_theory)">Cycle (graph theory)</a>.
%F A360854 a(n) = A288961(n) + A070968(n).
%F A360854 a(n) = 2*n*binomial(n,3) + Sum_{k=2..n} binomial(n,k)^2 * k! * (k-1)! / 2.
%o A360854 (PARI) a(n) = 2*n*binomial(n,3) + sum(k=2, n, binomial(n,k)^2 * k! * (k-1)!)/2
%Y A360854 Main diagonal of A360853.
%Y A360854 Cf. A070968, A234624, A288961, A360852.
%K A360854 nonn
%O A360854 1,3
%A A360854 _Andrew Howroyd_, Feb 24 2023