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 A302941 Number of total dominating sets in the 2n-crossed prism graph. 1

%I

%S 9,121,1296,14161,154449,1684804,18378369,200477281,2186871696,

%T 23855111401,260219353689,2838557779204,30963916217529,

%U 337764520613641,3684445810532496,40191139395243841,438418087537149729,4782407823513403204,52168067971110285489

%N Number of total dominating sets in the 2n-crossed prism graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CrossedPrismGraph.html">Crossed Prism Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,10,-1).

%F From _Andrew Howroyd_, Apr 16 2018: (Start)

%F G.f.: x*(9 + 31*x - 4*x^2)/((1 + x)*(1 - 11*x + x^2)).

%F a(n) = 10*a(n-1) + 10*a(n-2) - a(n-3) for n > 3.

%F a(n) = A006497(n)^2. (End)

%t Table[2 (-1)^n + ((11 - 3 Sqrt[13])/2)^n + ((11 + 3 Sqrt[13])/2)^n, {n, 20}] // FullSimplify

%t Table[LucasL[n, 3]^2, {n, 20}]

%t LucasL[Range[20], 3]^2

%t LinearRecurrence[{10, 10, -1}, {9, 121, 1296}, 20]

%t CoefficientList[Series[(9 + 31 x - 4 x^2)/(1 - 10 x - 10 x^2 + x^3), {x, 0, 20}], x]

%o (PARI) Vec((9 + 31*x - 4*x^2)/((1 + x)*(1 - 11*x + x^2)) + O(x^30)) \\ _Andrew Howroyd_, Apr 16 2018

%Y Cf. A006497, A287062, A291772, A302946.

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Apr 16 2018

%E a(1) and terms a(6) and beyond from _Andrew Howroyd_, Apr 16 2018

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Last modified May 29 16:43 EDT 2020. Contains 334704 sequences. (Running on oeis4.)