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 A287063 #21 Feb 16 2025 08:33:46
%S A287063 3,9,39,183,833,3629,15291,63051,256605,1036401,4167815,16720031,
%T A287063 66986169,268173525,1073185011,4293787923,17177379125,68714234201,
%U A287063 274866897279,1099488559527,4397998277073,17592085381629,70368534463019,281474540503643,1125899000873613
%N A287063 Number of dominating sets in the n-crown graph (for n > 1).
%C A287063 The 1-crown graph is the 2-empty graph bar K_2 which has a single dominating set and so differs from a(1) = 3. - _Eric W. Weisstein_, Sep 04 2021
%H A287063 Colin Barker, <a href="/A287063/b287063.txt">Table of n, a(n) for n = 1..1000</a>
%H A287063 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Crown Graph.html">Crown Graph</a>
%H A287063 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>
%H A287063 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-47,101,-116,68,-16).
%F A287063 a(n) = 4^n - 2^n*(n + 2) + n^2 + n + 3.
%F A287063 From _Colin Barker_, May 19 2017: (Start)
%F A287063 G.f.: x*(3 - 24*x + 81*x^2 - 126*x^3 + 92*x^4 - 32*x^5) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)).
%F A287063 a(n) = 11*a(n-1) - 47*a(n-2) + 101*a(n-3) - 116*a(n-4) + 68*a(n-5) - 16*a(n-6) for n>6.
%F A287063 (End)
%t A287063 Table[4^n - 2^n (n + 2) + n^2 + n + 3, {n, 25}]
%t A287063 LinearRecurrence[{11, -47, 101, -116, 68, -16}, {3, 9, 39, 183, 833, 3629}, 25]
%o A287063 (PARI) Vec( x*(3 - 24*x + 81*x^2 - 126*x^3 + 92*x^4 - 32*x^5) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)) + O(x^30)) \\ _Colin Barker_, May 19 2017
%K A287063 nonn,easy
%O A287063 1,1
%A A287063 _Eric W. Weisstein_, May 19 2017