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 A289254 #15 Feb 16 2025 08:33:48
%S A289254 0,9,54,243,1008,4077,16362,65511,262116,1048545,4194270,16777179,
%T A289254 67108824,268435413,1073741778,4294967247,17179869132,68719476681,
%U A289254 274877906886,1099511627715,4398046511040,17592186044349,70368744177594,281474976710583,1125899906842548
%N A289254 a(n) = 4^n - 3*n - 1.
%C A289254 Number of connected dominating sets in the n-cocktail party graph.
%H A289254 Colin Barker, <a href="/A289254/b289254.txt">Table of n, a(n) for n = 1..1000</a>
%H A289254 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CocktailPartyGraph.html">Cocktail Party Graph</a>
%H A289254 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>
%H A289254 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).
%F A289254 a(n) = 4^n - 3*n - 1.
%F A289254 a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-2).
%F A289254 G.f.: 9*x^2/((1-x)^2*(1-4*x)).
%F A289254 E.g.f.: exp(4*x) - (1+3*x)*exp(x). - _G. C. Greubel_, Mar 26 2022
%t A289254 Table[4^n - 3 n - 1, {n, 20}]
%t A289254 LinearRecurrence[{6, -9, 4}, {0, 9, 54}, 20]
%t A289254 CoefficientList[Series[-((9 x)/((-1 + x)^2 (-1 + 4 x))), {x, 0, 20}], x]
%o A289254 (PARI) concat(0, Vec(9*x^2 / ((1 - x)^2*(1 - 4*x)) + O(x^30))) \\ _Colin Barker_, Jun 30 2017
%o A289254 (Magma) [4^n -(3*n+1): n in [1..30]]; // _G. C. Greubel_, Mar 26 2022
%o A289254 (Sage) [4^n -(3*n+1) for n in (1..30)] # _G. C. Greubel_, Mar 26 2022
%Y A289254 Column 1 of A174266.
%K A289254 nonn,easy
%O A289254 1,2
%A A289254 _Eric W. Weisstein_, Jun 29 2017