A392620 - OEIS

%I #10 Feb 15 2026 09:46:07

%S 4,10,34,114,374,1222,3994,13058,42694,139590,456394,1492194,4878774,

%T 15951302,52153274,170516738,557509734,1822795270,5959685354,

%U 19485375074,63708034774,208295384582,681028184154,2226642652418,7280076826374,23802435716550,77822797691914

%N Number of maximal independent vertex sets in the n-necklace graph.

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

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,2).

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

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

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

%t RootSum[-2 + 3 # - 4 #^2 + #^3 &, #^Range[20] &]

%t LinearRecurrence[{4, -3, 2}, {4, 10, 34}, 20]

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

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Feb 15 2026