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%I #25 Feb 28 2020 08:16:36
%S 0,4,12,28,80,52,203,524,903,2184,3960,9628,20735,41619,93392,194732,
%T 425901,908791,1923408,4177488,8887289,19098160,40895771,87444572,
%U 187934955,401853599,861531618,1846051011,3953574901,8476042452,18151661911,38898045292
%N Number of minimal total dominating sets in the n-antiprism graph.
%C Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, Apr 15 2018
%H Andrew Howroyd, <a href="/A302763/b302763.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</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_23">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,4,5,8,-12,-23,-11,-11,8,37,23,-4,2,-7,-17,7,-7,-13,3,-1,-2,1).
%F G.f.: x^2*(4 + 12*x + 20*x^2 + 40*x^3 - 72*x^4 - 161*x^5 - 88*x^6 - 99*x^7 + 80*x^8 + 407*x^9 + 276*x^10 - 52*x^11 + 28*x^12 - 105*x^13 - 272*x^14 + 119*x^15 - 126*x^16 - 247*x^17 + 60*x^18 - 21*x^19 - 44*x^20 + 23*x^21)/(1 - 2*x^2 - 4*x^3 - 5*x^4 - 8*x^5 + 12*x^6 + 23*x^7 + 11*x^8 + 11*x^9 - 8*x^10 - 37*x^11 - 23*x^12 + 4*x^13 - 2*x^14 + 7*x^15 + 17*x^16 - 7*x^17 + 7*x^18 + 13*x^19 - 3*x^20 + x^21 + 2*x^22 - x^23). - _Andrew Howroyd_, Apr 15 2018
%t Table[RootSum[-1 + 2 # + #^2 - 3 #^3 + 13 #^4 + 7 #^5 - 7 #^6 + 17 #^7 + 7 #^8 - 2 #^9 + 4 #^10 - 23 #^11 - 37 #^12 - 8 #^13 + 11 #^14 + 11 #^15 + 23 #^16 + 12 #^17 - 8 #^18 - 5 #^19 - 4 #^20 - 2 #^21 + #^23 &, #^n &], {n, 30}]
%t RootSum[-1 + 2 # + #^2 - 3 #^3 + 13 #^4 + 7 #^5 - 7 #^6 + 17 #^7 + 7 #^8 - 2 #^9 + 4 #^10 - 23 #^11 - 37 #^12 - 8 #^13 + 11 #^14 + 11 #^15 + 23 #^16 + 12 #^17 - 8 #^18 - 5 #^19 - 4 #^20 - 2 #^21 + #^23 &, #^Range[30] &]
%t LinearRecurrence[{0, 2, 4, 5, 8, -12, -23, -11, -11, 8, 37, 23, -4, 2, -7, -17, 7, -7, -13, 3, -1, -2, 1}, {0, 4, 12, 28, 80, 52, 203, 524, 903, 2184, 3960, 9628, 20735, 41619, 93392, 194732, 425901, 908791, 1923408, 4177488, 8887289, 19098160, 40895771}, 40]
%Y Cf. A290377, A302255, A302652, A302760.
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Apr 12 2018
%E a(1)-a(2) and terms a(11) and beyond from _Andrew Howroyd_, Apr 15 2018
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