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 A302941 Number of total dominating sets in the 2n-crossed prism graph. 1
 9, 121, 1296, 14161, 154449, 1684804, 18378369, 200477281, 2186871696, 23855111401, 260219353689, 2838557779204, 30963916217529, 337764520613641, 3684445810532496, 40191139395243841, 438418087537149729, 4782407823513403204, 52168067971110285489 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Eric Weisstein's World of Mathematics, Crossed Prism Graph Eric Weisstein's World of Mathematics, Total Dominating Set Index entries for linear recurrences with constant coefficients, signature (10,10,-1). FORMULA From Andrew Howroyd, Apr 16 2018: (Start) G.f.: x*(9 + 31*x - 4*x^2)/((1 + x)*(1 - 11*x + x^2)). a(n) = 10*a(n-1) + 10*a(n-2) - a(n-3) for n > 3. a(n) = A006497(n)^2. (End) MATHEMATICA Table[2 (-1)^n + ((11 - 3 Sqrt[13])/2)^n + ((11 + 3 Sqrt[13])/2)^n, {n, 20}] // FullSimplify Table[LucasL[n, 3]^2, {n, 20}] LucasL[Range[20], 3]^2 LinearRecurrence[{10, 10, -1}, {9, 121, 1296}, 20] CoefficientList[Series[(9 + 31 x - 4 x^2)/(1 - 10 x - 10 x^2 + x^3), {x, 0, 20}], x] PROG (PARI) Vec((9 + 31*x - 4*x^2)/((1 + x)*(1 - 11*x + x^2)) + O(x^30)) \\ Andrew Howroyd, Apr 16 2018 CROSSREFS Cf. A006497, A287062, A291772, A302946. Sequence in context: A017102 A167722 A103930 * A183514 A138978 A046184 Adjacent sequences:  A302938 A302939 A302940 * A302942 A302943 A302944 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Apr 16 2018 EXTENSIONS a(1) and terms a(6) and beyond from Andrew Howroyd, Apr 16 2018 STATUS approved

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)