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%I #23 Apr 17 2018 12:11:56
%S 1,11,49,131,441,1499,5041,17155,58081,196331,664225,2246915,7601049,
%T 25714875,86992929,294294531,995591809,3368061131,11394068049,
%U 38545859971,130399709881,441139059867,1492362754129,5048627019523,17079382863841,57779138374059
%N Number of total dominating sets in the n-Moebius ladder.
%C Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, Apr 16 2018
%H Andrew Howroyd, <a href="/A295420/b295420.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</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_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,4,-2,10,4,0,-1,-1).
%F From _Andrew Howroyd_, Apr 16 2018: (Start)
%F G.f.: x*(1 - x)*(1 + 9*x + 25*x^2 + 5*x^3 + 11*x^4 + 3*x^5 + 7*x^6 + 3*x^7)/((1 - x + x^2 + x^3)*(1 + x + x^2 - x^3)*(1 - 3*x - x^2 - x^3)).
%F a(n) = 3*a(n-1) + 4*a(n-3) - 2*a(n-4) + 10*a(n-5) + 4*a(n-6) - a(n-8) - a(n-9) for n > 9. (End)
%t Table[RootSum[-1 - # - 3 #^2 + #^3 &, #^n &] - RootSum[1 + # - #^2 + #^3 &, #^n &] + RootSum[-1 + # + #^2 + #^3 &, #^n &], {n, 20}]
%t LinearRecurrence[{3, 0, 4, -2, 10, 4, 0, -1, -1}, {1, 11, 49, 131, 441, 1499, 5041, 17155, 58081}, 20]
%t CoefficientList[Series[(1 + 8 x + 16 x^2 - 20 x^3 + 6 x^4 - 8 x^5 + 4 x^6 - 4 x^7 - 3 x^8)/(1 - 3 x - 4 x^3 + 2 x^4 - 10 x^5 - 4 x^6 + x^8 + x^9), {x, 0, 20}], x]
%o (PARI) Vec((1 - x)*(1 + 9*x + 25*x^2 + 5*x^3 + 11*x^4 + 3*x^5 + 7*x^6 + 3*x^7)/((1 - x + x^2 + x^3)*(1 + x + x^2 - x^3)*(1 - 3*x - x^2 - x^3)) + O(x^30)) \\ _Andrew Howroyd_, Apr 16 2018
%Y Cf. A284663, A290337.
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Apr 16 2018
%E a(1)-a(2) and terms a(10) and beyond from _Andrew Howroyd_, Apr 16 2018
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