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%I
%S 3,21,48,161,473,1476,4553,14241,44688,141081,447153,1422596,4539473,
%T 14522361,46556048,149508801,480810153,1548053316,4988972313,
%U 16090635281,51928966928,167675418921,541639730273,1750245266436,5657268819873,18289912673001
%N Number of total dominating sets in the n-gear graph.
%C Extended to a(1)-a(2) using the formula/recurrence.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GearGraph.html">Gear 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_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,2,-13,-6,4).
%F a(n) = 2*(-1)^n + 2^n*A000032(n) + A005248(n).
%F a(n) = 4*a(n-1) + 2*a(n-2) - 13*a(n-3) - 6*a(n-4) + 4*a(n-5).
%F G.f.: -x*(3+9*x-42*x^2-34*x^3+24*x^4) / ( (1+x)*(x^2-3*x+1)*(4*x^2+2*x-1) ).
%t Table[2 (-1)^n + 2^n LucasL[n] + LucasL[2 n], {n, 20}]
%t LinearRecurrence[{4, 2, -13, -6, 4}, {3, 21, 48, 161, 473}, 20]
%t CoefficientList[Series[(-3 - 9 x + 42 x^2 + 34 x^3 - 24 x^4)/(-1 + 4 x + 2 x^2 - 13 x^3 - 6 x^4 + 4 x^5), {x, 0, 20}], x]
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, May 02 2018
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