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 A290756 #18 Feb 16 2025 08:33:50
%S A290756 7,60,499,4062,32689,261972,2096791,16776474,134216221,1073738784,
%T A290756 8589928483,68719464486,549755789353,4398046461996,35184371990575,
%U A290756 281474976514098,2251799813292085,18014398508695608,144115188074283067,1152921504603701310
%N A290756 Number of (non-null) connected induced subgraphs of the complete tripartite graph K_{n,n,n}.
%C A290756 The only disconnected induced subgraphs are those constructed from the vertices of a single partition. - _Andrew Howroyd_, Aug 10 2017
%H A290756 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>
%H A290756 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H A290756 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>
%H A290756 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12, -37, 42, -16).
%F A290756 a(n) = 8^n - 3*2^n + 3*n + 2. - _Andrew Howroyd_, Aug 10 2017
%F A290756 a(n) = 12*a(n-1) - 37*a(n-2) + 42*a(n-3) - 16*a(n-4).
%F A290756 G.f.: (x (7 - 24 x + 38 x^2))/((-1 + x)^2 (1 - 10 x + 16 x^2)).
%t A290756 Table[8^n - 3 2^n + 3 n + 2, {n, 20}]
%t A290756 LinearRecurrence[{12, -37, 42, -16}, {7, 60, 499, 4062}, 20]
%t A290756 CoefficientList[Series[(7 - 24 x + 38 x^2)/((-1 + x)^2 (1 - 10 x + 16 x^2)), {x, 0, 20}], x]
%o A290756 (PARI) a(n) = 8^n - 3*2^n + 3*n + 2; \\ _Andrew Howroyd_, Aug 10 2017
%Y A290756 Cf. A286191.
%K A290756 nonn,easy
%O A290756 1,1
%A A290756 _Eric W. Weisstein_, Aug 09 2017
%E A290756 a(7)-a(20) from _Andrew Howroyd_, Aug 10 2017