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A242985 a(n) = 4^n + 2^(n+1).

%I A242985 #28 Feb 16 2025 08:33:22
%S A242985 3,8,24,80,288,1088,4224,16640,66048,263168,1050624,4198400,16785408,
%T A242985 67125248,268468224,1073807360,4295098368,17180131328,68720001024,
%U A242985 274878955520,1099513724928,4398050705408,17592194433024,70368760954880,281475010265088,1125899973951488
%N A242985 a(n) = 4^n + 2^(n+1).
%C A242985 Subsequence of A088966.
%C A242985 For n > 1, number of connected dominating sets in the n-book graph. - _Eric W. Weisstein_, Jun 29 2017
%H A242985 Jens Kruse Andersen, <a href="/A242985/b242985.txt">Table of n, a(n) for n = 0..100</a>
%H A242985 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BookGraph.html">Book Graph</a>
%H A242985 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>
%H A242985 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -8).
%F A242985 a(n) = A000302(n) + A000079(n+1).
%F A242985 G.f.: 1/(1-4*x) + 2/(1-2*x). - _Robert Israel_, Aug 17 2014
%F A242985 E.g.f.: exp(4*x) + 2*exp(2*x). - _G. C. Greubel_, Jan 11 2020
%e A242985 a(0) = 4^0 + 2^1 = 1 + 2 = 3.
%p A242985 seq( 4^n + 2^(n+1), n=0..30); # _G. C. Greubel_, Jan 11 2020
%t A242985 (* From _Eric W. Weisstein_, Jun 29 2017: (Start) *)
%t A242985 Table[4^n + 2^(n+1), {n, 0, 30}]
%t A242985 LinearRecurrence[{6,-8}, {8,24}, {0, 30}]
%t A242985 CoefficientList[Series[(3-10x)/((1-2x)(1-4x)), {x, 0, 30}], x] (* End *)
%o A242985 (PARI) a(n) = 4^n + 2^(n+1);
%o A242985 (Magma) [4^n + 2^(n+1): n in [0..30]]; // _G. C. Greubel_, Jan 11 2020
%o A242985 (Sage) [4^n + 2^(n+1) for n in (0..30)] # _G. C. Greubel_, Jan 11 2020
%o A242985 (GAP) List([0..30], n-> 4^n + 2^(n+1)); # _G. C. Greubel_, Jan 11 2020
%Y A242985 Cf. A000079, A000302, A088966.
%K A242985 nonn
%O A242985 0,1
%A A242985 _Michel Marcus_, Aug 17 2014