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%I #19 Sep 19 2021 13:07:02
%S 0,3,5,7,14,22,42,70,127,218,388,675,1191,2083,3663,6420,11275,19777,
%T 34716,60912,106904,187592,329213,577716,1013834,1779141,3122189,
%U 5479045,9615069,16873254,29610513,51962811,91188394,160024458,280823366,492810634,864822395
%N Number of minimal total dominating sets in the (2n-1)-triangular snake graph.
%H Andrew Howroyd, <a href="/A308591/b308591.txt">Table of n, a(n) for n = 1..1000</a>
%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_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,1,1).
%F From _Andrew Howroyd_, Sep 08 2019: (Start)
%F a(n) = 2*a(n-2) + a(n-3) + a(n-4) + a(n-5) for n > 7.
%F G.f.: x^2*(3 + 5*x + x^2 + x^3 - x^5)/((1 + x)^2*(1 - 2*x + x^2 - x^3)).
%F (End)
%t Join[{0, 3}, Table[((3 - 5 n) (-1)^n + RootSum[-1 + # - 2 #^2 + #^3 &, -2 #^n + 249 #^(n + 1) + 7 #^(n + 2) &]/23)/25, {n, 3, 20}]] (* _Eric W. Weisstein_, Sep 19 2021 *)
%t Join[{0, 3}, LinearRecurrence[{0, 2, 1, 1, 1}, {5, 7, 14, 22, 42}, 20]] (* _Eric W. Weisstein_, Sep 19 2021 *)
%t CoefficientList[Series[x (-3 - 5 x - x^2 - x^3 + x^5)/((1 + x)^2 (-1 + 2 x - x^2 + x^3)), {x, 0, 20}], x] (* _Eric W. Weisstein_, Sep 19 2021 *)
%o (PARI) concat([0], Vec((3 + 5*x + x^2 + x^3 - x^5)/((1 + x)^2*(1 - 2*x + x^2 - x^3)) + O(x^40))) \\ _Andrew Howroyd_, Sep 08 2019
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Jun 09 2019
%E Terms a(11) and beyond from _Andrew Howroyd_, Sep 08 2019
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