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A297712 Number of irredundant sets in the n-dipyramidal graph. 1

%I

%S 7,22,29,39,60,94,151,241,400,671,1135,1924,3277,5598,9575,16389,

%T 28067,48089,82411,141246,242102,414999,711394,1219497,2090527,

%U 3583720,6143480,10531637,18054187,30949982,53057055,90954885,155922576,267295733,458221102,785521661

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal 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_08">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -1, 2, -2, 0, 2, -1).

%F a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 2*a(n-4) - 2*a(n-5) + 2*a(n-7) - a(n-8) for n > 11.

%F G.f.: x^3*(7 + x - 23*x^2 + 3*x^3 + 9*x^4 - 9*x^5 + 14*x^6 + 2*x^7 - 6*x^8)/((-1 + x)^2*(1 - x - x^2 - x^4 + x^6)).

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

%t Join[{7}, LinearRecurrence[{3, -2, -1, 2, -2, 0, 2, -1}, {22, 29, 39, 60, 94, 151, 241, 400}, 20]]

%t CoefficientList[Series[(7 + x - 23 x^2 + 3 x^3 + 9 x^4 - 9 x^5 + 14 x^6 + 2 x^7 - 6 x^8)/((-1 + x)^2 (1 - x - x^2 - x^4 + x^6)), {x, 0, 20}], x]

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Jun 18 2018

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Last modified November 28 00:12 EST 2021. Contains 349395 sequences. (Running on oeis4.)