A287498 - OEIS

%I #12 Feb 16 2025 08:33:46

%S 0,4,9,12,30,55,105,212,405,794,1551,3015,5889,11477,22374,43636,

%T 85068,165871,323418,630582,1229517,2397289,4674198,9113711,17769780,

%U 34647305,67554891,131717661,256821477,500747300

%N Number of maximal independent vertex sets (and minimal vertex covers) in the n-web 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/WebGraph.html">Web Graph</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,3,1).

%F G.f.: x^2*(-4 - 9*x - 4*x^2)/(-1 + 2*x^2 + 3*x^3 + x^4).

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

%t Table[RootSum[-1 - 3 # - 2 #^2 + #^4 &, #^n &], {n, 20}]

%t LinearRecurrence[{0, 2, 3, 1}, {0, 4, 9, 12}, 20]

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, May 25 2017