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%I #23 Sep 08 2022 08:46:21
%S 2,0,0,4,16,44,104,228,480,988,2008,4052,8144,16332,32712,65476,
%T 131008,262076,524216,1048500,2097072,4194220,8388520,16777124,
%U 33554336,67108764,134217624,268435348,536870800,1073741708,2147483528,4294967172,8589934464
%N a(n) = 4 + 2^n - 4*n.
%C a(n) is the number of connected dominating sets and total dominating sets in the n-path complement graph for n > 1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PathComplementGraph.html">Path Complement Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F G.f.: -2*x*(1 - 4*x + 5*x^2)/((-1 + x)^2*(-1 + 2*x)).
%F a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
%F a(n) = A258547(n-5) for n > 5 (conjectured).
%F a(n) = 4 * A000295(n) for n > 1. - _Alois P. Heinz_, Apr 12 2018
%t Table[4 + 2^n - 4 n, {n, 20}]
%t LinearRecurrence[{4, -5, 2}, {2, 0, 0}, 20]
%t CoefficientList[Series[-(2 (1 - 4 x + 5 x^2)/((-1 + x)^2 (-1 + 2 x))), {x, 0, 20}], x]
%o (PARI) a(n) = 4+2^n-4*n; \\ _Altug Alkan_, Apr 12 2018
%o (Magma) [4+2^n-4*n : n in [1..45]]; // _Vincenzo Librandi_, Apr 13 2018
%Y Cf. A258547.
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Apr 11 2018
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