A290612 - OEIS

%I #7 Feb 16 2025 08:33:50

%S 4,3,6,6,8,11,13,18,23,30,40,52,69,91,120,159,210,278,368,487,645,854,

%T 1131,1498,1984,2628,3481,4611,6108,8091,10718,14198,18808,24915,

%U 33005,43722,57919,76726,101640,134644,178365,236283,313008,414647,549290,727654,963936

%N Number of maximal independent vertex sets (and minimal vertex covers) in the n-wheel graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalVertexCover.html">Minimal Vertex Cover</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, -1).

%F a(n) = a(n-1) + a(n-2) - a(n-4).

%F G.f.: (x^3 (4 - x - x^2 - 3 x^3))/(1 - x - x^2 + x^4).

%t Table[1 + RootSum[-1 - # + #^3 &, #^(n - 1) &], {n, 4, 20}]

%t LinearRecurrence[{1, 1, 0, -1}, {4, 3, 6, 6, 8}, 20]

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

%K nonn

%O 4,1

%A _Eric W. Weisstein_, Aug 07 2017