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Number of total dominating sets in the wheel graph on n nodes.
3

%I #6 Jan 08 2020 10:28:57

%S 4,2,4,11,24,42,79,156,304,587,1144,2246,4419,8712,17224,34131,67744,

%T 134642,267919,533636,1063704,2121627,4233904,8452686,16880899,

%U 33722192,67380304,134656931,269146104,538020762,1075602319,2150493996,4299838144,8597815787

%N Number of total dominating sets in the wheel graph on n nodes.

%C Extended to a(1)-a(3) using the formula/recurrence.

%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/WheelGraph.html">Wheel Graph</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, -5, 3, -2, -1, 2).

%F a(n) = A000032(n - 1) + 2*sin(n*Pi/2) + 2^(n - 1) - 1.

%F a(n) = 4*a(n-1) - 5*a(n-2) + 3*a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6).

%F G.f.: x*(-4+14*x-16*x^2+7*x^3+3*x^5-2*x^4) / ( (x-1)*(2*x-1)*(x^2+x-1)*(x^2+1) ).

%t Table[LucasL[n - 1] + 2 Sin[n Pi/2] + 2^(n - 1) - 1, {n, 20}]

%t LinearRecurrence[{4, -5, 3, -2, -1, 2}, {4, 2, 4, 11, 24, 42}, 20]

%t CoefficientList[Series[(-4 + 14 x - 16 x^2 + 7 x^3 - 2 x^4 + 3 x^5)/(-1 + 4 x - 5 x^2 + 3 x^3 - 2 x^4 - x^5 + 2 x^6), {x, 0, 20}], x]

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Apr 10 2018