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 A291593 #17 Feb 16 2025 08:33:50
%S A291593 1,6,397,64627,33548446,68719441230,562949953224709,
%T A291593 18446744073708514623,2417851639229258344134994,
%U A291593 1267650600228229401496677070990,2658455991569831745807614120434011325,22300745198530623141535718272648360902487971
%N A291593 Number of (non-null) connected induced subgraphs in the n X n rook complement graph.
%C A291593 From _Andrew Howroyd_, Aug 30 2017: (Start)
%C A291593 The vertex sets inducing disconnected subgraphs are:
%C A291593 - two or more vertices taken from a single row or column,
%C A291593 - any vertex combined with at least one from the same row and at least one from the same column,
%C A291593 - four vertices forming the corners of a rectangle. (End)
%H A291593 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H A291593 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H A291593 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>
%F A291593 a(n) = 2^(n^2) - 2*n*(2^n-n-1) - n^2*(2^(n-1)-1)^2 - binomial(n,2)^2 - 1. - _Andrew Howroyd_, Aug 30 2017
%t A291593 Table[2^(n^2) - 2 n (2^n - n - 1) - n^2 (2^(n - 1) - 1)^2 - Binomial[n, 2]^2 - 1, {n, 10}]
%o A291593 (PARI) a(n) = 2^(n^2) - 2*n*(2^n-n-1) - n^2*(2^(n-1)-1)^2 - binomial(n,2)^2 - 1; \\ _Andrew Howroyd_, Aug 30 2017
%K A291593 nonn
%O A291593 1,2
%A A291593 _Eric W. Weisstein_, Aug 27 2017
%E A291593 a(6)-a(12) from _Andrew Howroyd_, Aug 30 2017