%I #13 Sep 03 2021 13:59:11
%S 1,4,16,46,148,466,1468,4630,14596,46018,145084,457414,1442116,
%T 4546642,14334460,45193078,142482820,449213794,1416262204,4465131430,
%U 14077477060,44382872818,139928439676,441160451926,1390871968516,4385082172162,13825101153724
%N Number of total dominating sets in the (2n-1)-triangular snake (for n > 1).
%C 1-triangular snake = K_1 has no total dominating sets and so its count (0) differs from a(1) = 1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularSnakeGraph.html">Triangular Snake Graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,2).
%F a(n) = 2*a(n-1) + 3*a(n-2) + 2*a(n-3).
%F G.f.: x*(-1 - 2*x - 5*x^2)/(-1 + 2*x + 3*x^2 + 2*x^3).
%t Table[RootSum[-2 - 3 # - 2 #^2 + #^3 &, 65 #^n - 100 #^(n + 1) + 31 #^(n + 2) &]/122, {n, 20}]
%t LinearRecurrence[{2, 3, 2}, {1, 4, 16}, 20]
%t CoefficientList[Series[(-1 - 2 x - 5 x^2)/(-1 + 2 x + 3 x^2 + 2 x^3), {x, 0, 20}], x]
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Jun 09 2019