login
Number of maximal independent vertex sets (and minimal vertex covers) in the n-antiprism graph.
0

%I #6 Aug 10 2017 15:05:02

%S 3,12,15,31,49,92,156,279,484,855,1495,2629,4608,8092,14195,24916,

%T 43719,76727,134641,236284,414644,727655,1276940,2240879,3932463,

%U 6900997,12110400,21252276,37295139,65448412,114853951,201554639,353703729,620706780,1089264460,1911525879

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

%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/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalVertexCover.html">Minimal Vertex Cover</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 (-3 - 9 x - 4 x^3))/(-1 + x + x^2 + x^4).

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

%t LinearRecurrence[{1, 1, 0, 1}, {3, 12, 15, 31}, 20]

%t CoefficientList[Series[(-3 - 9 x - 4 x^3)/(-1 + x + x^2 + x^4), {x, 0, 20}], x]

%K nonn

%O 3,1

%A _Eric W. Weisstein_, Aug 07 2017