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A302658 Number of minimal total dominating sets in the wheel graph on n nodes.

%I A302658 #24 Jun 11 2025 19:55:33
%S A302658 1,2,6,8,10,15,14,12,21,35,33,37,52,63,83,116,136,162,228,309,388,506,
%T A302658 667,865,1155,1547,2010,2629,3509,4654,6138,8132,10750,14195,18842,
%U A302658 25000,33041,43719,57957,76769,101680,134731,178407,236240,313052,414782,549336
%N A302658 Number of minimal total dominating sets in the wheel graph on n nodes.
%C A302658 Wheel graphs are defined for n>=4; extended to n=2 using formula. - _Andrew Howroyd_, Apr 15 2018
%H A302658 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalTotalDominatingSet.html">Minimal Total Dominating Set</a>.
%H A302658 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>.
%H A302658 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1,0,0,-1,0,1,1,-1).
%F A302658 a(n) = A300738(n-1) + (n-1). - _Andrew Howroyd_, Apr 15 2018
%F A302658 G.f.: x^2*(1 + 3*x^2 - 3*x^3 - x^4 - x^5 - 8*x^6 - 2*x^7 + 8*x^8 + 11*x^9 - 9*x^10)/((-1 + x)^2*(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)).
%t A302658 Table[n - 1 + RootSum[-1 - # + #^3 &, #^(n - 1) &] + (1 - (-1)^n) RootSum[-1 + #^2 + #^3 &, #^((n - 1)/2) &], {n, 2, 50}]
%t A302658 LinearRecurrence[{2, -1, 1, -1, 0, 0, -1, 0, 1, 1, -1}, {1, 2, 6, 8, 10, 15, 14, 12, 21, 35, 33}, 50]
%t A302658 CoefficientList[Series[(1 + 3 x^2 - 3 x^3 - x^4 - x^5 - 8 x^6 - 2 x^7 + 8 x^8 + 11 x^9 - 9 x^10)/((-1 + x)^2 (1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)), {x, 0, 50}], x]
%o A302658 (PARI) {my(v=concat([0,0],Vec((3 + 4*x + 5*x^2 + 6*x^3 - 8*x^5 - 9*x^6)/((1 - x^2 - x^3)*(1 + x^2 - x^6)) + O(x^50))));vector(#v,i,v[i]+i)} \\ _Andrew Howroyd_, Apr 15 2018
%Y A302658 Cf. A213661, A290270, A300738, A302603.
%K A302658 nonn
%O A302658 2,2
%A A302658 _Eric W. Weisstein_, Apr 11 2018
%E A302658 a(2)-a(3) and terms a(20) and beyond from _Andrew Howroyd_, Apr 15 2018