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 A302761 #33 Feb 16 2025 08:33:53
%S A302761 1,4,23,136,707,3312,14527,61264,252515,1027192,4147343,16674984,
%T A302761 66887875,267960544,1072726271,4292804896,17175281987,68709777768,
%U A302761 274857460111,1099468636600,4397956334051,17591997301264,70368349913663,281474154627696,1125898195567267
%N A302761 Number of total dominating sets in the n-barbell graph.
%H A302761 Colin Barker, <a href="/A302761/b302761.txt">Table of n, a(n) for n = 1..1000</a>
%H A302761 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarbellGraph.html">Barbell Graph</a>
%H A302761 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
%H A302761 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-47,101,-116,68,-16).
%F A302761 a(n) = (2^n-n)^2 - (2^n-2*n). - _Andrew Howroyd_, Apr 14 2018
%F A302761 From _Colin Barker_, Apr 15 2018: (Start)
%F A302761 G.f.: x*(1 - 7*x + 26*x^2 - 30*x^3 + 4*x^4) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)).
%F A302761 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. (End)
%F A302761 E.g.f.: exp(x)*(exp(3*x) + x*(3 + x) - exp(x)*(1 + 4*x)). - _Stefano Spezia_, Sep 06 2023
%t A302761 Array[(2^# - #)^2 - (2^# - 2 #) &, 30] (* _Michael De Vlieger_, Apr 14 2018 *)
%t A302761 Table[(2^n - n)^2 - (2^n - 2*n), {n, 30}]
%t A302761 LinearRecurrence[{11, -47, 101, -116, 68, -16}, {1, 4, 23, 136, 707, 3312}, 30]
%t A302761 CoefficientList[Series[(1 - 7 x + 26 x^2 - 30 x^3 + 4 x^4)/((-1 + x)^3 (-1 + 2 x)^2 (-1 + 4 x)), {x, 0, 30}], x] (* _Eric W. Weisstein_, Apr 16 2018 *)
%o A302761 (PARI) a(n)={(2^n-n)^2 - (2^n-2*n)} \\ _Andrew Howroyd_, Apr 14 2018
%o A302761 (PARI) Vec(x*(1 - 7*x + 26*x^2 - 30*x^3 + 4*x^4) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)) + O(x^30)) \\ _Colin Barker_, Apr 15 2018
%o A302761 (Magma) [(2^n-n)^2 - (2^n-2*n): n in [1..30]]; // _Vincenzo Librandi_, Apr 15 2018
%Y A302761 Cf. A060867, A302650.
%K A302761 nonn,easy
%O A302761 1,2
%A A302761 _Eric W. Weisstein_, Apr 12 2018
%E A302761 a(1)-a(2) and a(11)-a(25) from _Andrew Howroyd_, Apr 14 2018