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 A289255 #32 Jul 13 2025 13:11:00
%S A289255 1,11,57,247,1013,4083,16369,65519,262125,1048555,4194281,16777191,
%T A289255 67108837,268435427,1073741793,4294967263,17179869149,68719476699,
%U A289255 274877906905,1099511627735,4398046511061,17592186044371,70368744177617,281474976710607,1125899906842573
%N A289255 a(n) = 4^n - 2*n - 1.
%C A289255 Number of dominating sets in the n-cocktail party graph.
%H A289255 Colin Barker, <a href="/A289255/b289255.txt">Table of n, a(n) for n = 1..1000</a>
%H A289255 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CocktailPartyGraph.html">Cocktail Party Graph</a>.
%H A289255 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>.
%H A289255 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).
%F A289255 a(n) = 4^n - 2*n - 1.
%F A289255 a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).
%F A289255 G.f.: (-1 - 5*x)*x/((-1 + x)^2*(-1 + 4*x)).
%F A289255 From _Elmo R. Oliveira_, Apr 02 2025: (Start)
%F A289255 E.g.f.: exp(x)*(exp(3*x) - (2*x + 1)).
%F A289255 a(n) = A000302(n) - A005408(n). (End)
%t A289255 Table[4^n - 2 n - 1, {n, 20}]
%t A289255 LinearRecurrence[{6, -9, 4}, {1, 11, 57}, 20]
%t A289255 CoefficientList[Series[(-1 - 5 x)/((-1 + x)^2 (-1 + 4 x)), {x, 0, 20}], x]
%o A289255 (PARI) Vec(x*(1 + 5*x) / ((1 - x)^2*(1 - 4*x)) + O(x^30)) \\ _Colin Barker_, Jun 30 2017
%Y A289255 Cf. A000302, A005408, A096046 (first differences).
%K A289255 nonn,easy
%O A289255 1,2
%A A289255 _Eric W. Weisstein_, Jun 29 2017