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%I #15 Jan 03 2023 04:20:51
%S 2,3,7,12,17,27,46,75,119,192,313,507,818,1323,2143,3468,5609,9075,
%T 14686,23763,38447,62208,100657,162867,263522,426387,689911,1116300,
%U 1806209,2922507,4728718,7651227,12379943,20031168,32411113,52442283,84853394,137295675
%N Number of total dominating sets in the n-pan 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/PanGraph.html">Pan 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_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1).
%F 5*a(n) = 3*A000032(n+2) + 6*cos(n*Pi/2) - 2*sin(n*Pi/2).
%F a(n) = a(n-1) + a(n-2) + a(n-3) for n > 3.
%F G.f.: -x*(2 + x + 4*x^2 + 3*x^3)/((1 + x^2)*(x^2 + x - 1)).
%F E.g.f.: (6*cos(x) - 2*sin(x) - 15 + 3*exp(x/2)*(3*cosh(sqrt(5)*x/2) + sqrt(5)*sinh(sqrt(5)*x/2)))/5. - _Stefano Spezia_, Jan 03 2023
%t Table[(3 LucasL[n + 2] + 6 Cos[n Pi/2] - 2 Sin[n Pi/2])/5, {n, 20}]
%t LinearRecurrence[{1, 0, 1, 1}, {2, 3, 7, 12}, 20]
%t CoefficientList[Series[(-2 - x - 4 x^2 - 3 x^3)/(-1 + x + x^3 + x^4), {x, 0, 20}], x]
%Y Cf. A000032.
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Apr 09 2018