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%I #13 Oct 30 2024 11:31:18
%S 3,15,27,48,75,108,147,192,243,300,363,432,507,588,675,768,867,972,
%T 1083,1200,1323,1452,1587,1728,1875,2028,2187,2352,2523,2700,2883,
%U 3072,3267,3468,3675,3888,4107,4332,4563,4800,5043,5292,5547,5808,6075,6348,6627
%N Number of minimum dominating sets in the complete tripartite graph K_{n,n,n}.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A033428(n) = 3*n^2 for n != 2.
%F G.f.: 3*x*(-1 - 2*x + 3*x^2 - 3*x^3 + x^4)/(-1 + x)^3.
%F From _Stefano Spezia_, Sep 06 2021: (Start)
%F E.g.f.: 3*x*(x + 2*exp(x)*(1 + x))/2.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 5. (End)
%Y Cf. A291537, A290325.
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Sep 05 2021