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%I #14 Aug 13 2017 09:53:43
%S 5,13,35,113,355,1105,3435,10625,32723,100433,307323,937985,2856547,
%T 8682897,26349835,79850241,241679859,730700881,2207155867,6661493633,
%U 20090908803,60555714705,182419600683,549259559297,1653098625555,4973441442385,14957936920763
%N Number of irredundant sets in the n-helm graph.
%C Extended to a(1)-a(2) using the recurrence.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HelmGraph.html">Helm Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IrredundantSet.html">Irredundant Set</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6, -10, 4, -5, 6).
%F a(n) = 6*a(n-1) - 10*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5).
%F G.f.: (x (-5 + 17 x - 7 x^2 - 13 x^3))/(-1 + 6 x - 10 x^2 + 4 x^3 - 5 x^4 + 6 x^5).
%t Table[1 + 2 3^n - RootSum[-2 - # - 2 #^2 + #^3 &, #^n &], {n, 20}]
%t LinearRecurrence[{6, -10, 4, -5, 6}, {5, 13, 35, 113, 355}, 20]
%t CoefficientList[Series[(-5 + 17 x - 7 x^2 - 13 x^3)/(-1 + 6 x - 10 x^2 + 4 x^3 - 5 x^4 + 6 x^5), {x, 0, 20}], x]
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Aug 07 2017
%E a(12)-a(16) from _Andrew Howroyd_, Aug 11 2017