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%I #13 Mar 04 2024 00:02:16
%S 2,2,3,5,7,8,13,18,25,34,49,69,95,134,188,264,368,517,725,1015,1422,
%T 1993,2794,3913,5484,7685,10769,15089,21144,29630,41518,58178,81523,
%U 114237,160075,224308,314317,440442,617177,864830,1211861,1698141,2379551,3334390,4672376
%N Number of minimal dominating sets in the n-pan graph.
%C Extended to a(1)-a(2) using the recurrence.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PanGraph.html">Pan Graph</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 1, 0, -1).
%F a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-6).
%F G.f.: x*(2 + 2*x + x^2 + x^3 - 2*x^5)/(1 - x^2 - x^3 - x^4 + x^6).
%t Table[-RootSum[1 - #^2 - #^3 - #^4 + #^6 &, -9 #^n + 33 #^(n + 1) - 23 #^(n + 2) - 45 #^(n + 3) - 38 #^(n + 4) + #^(n + 5) &]/229, {n, 20}]
%t LinearRecurrence[{0, 1, 1, 1, 0, -1}, {2, 2, 3, 5, 7, 8}, 50]
%t CoefficientList[Series[(2 + 2 x + x^2 + x^3 - 2 x^5)/(1 - x^2 - x^3 - x^4 + x^6), {x, 0, 20}], x]
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Jul 25 2017
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