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A290494 Number of irredundant sets in the n-wheel graph. 1

%I

%S 5,12,17,25,44,76,131,219,376,645,1107,1894,3245,5564,9539,16351,

%T 28027,48047,82367,141200,242054,414949,711342,1219443,2090471,

%U 3583662,6143420,10531575,18054123,30949916,53056987,90954815,155922504,267295659,458221026

%N Number of irredundant sets in the n-wheel graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IrredundantSet.html">Irredundant 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_07">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -1, 1, -1, -1, 1).

%F a(n)=2*a(n-1)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+a(n-7).

%F G.f.: -x^4*(5+2*x-7*x^2-4*x^3+x^4-2*x^5+4*x^6) / ( (x-1)*(x^6-x^4-x^2-x+1) ).

%t Table[1 - RootSum[1 - #^2 - #^4 - #^5 + #^6 &, -2 #^(n + 3) - #^(n + 4) - #^(n + 6) + #^(n + 7) &], {n, 4, 20}]

%t LinearRecurrence[{2, 0, -1, 1, -1, -1, 1}, {5, 12, 17, 25, 44, 76, 131}, 20]

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

%K nonn

%O 4,1

%A _Eric W. Weisstein_, Aug 04 2017

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Last modified June 23 05:05 EDT 2021. Contains 345395 sequences. (Running on oeis4.)