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 A302946 Number of minimal (and minimum) total dominating sets in the 2n-crossed prism graph. 2
 4, 36, 196, 1156, 6724, 39204, 228484, 1331716, 7761796, 45239076, 263672644, 1536796804, 8957108164, 52205852196, 304278004996, 1773462177796, 10336495061764, 60245508192804, 351136554095044, 2046573816377476, 11928306344169796, 69523264248641316 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Extended to a(1) using the formula/recurrence. Since minimal and minimum total dominating sets are equivalent, the crossed prism graphs could be said to be "well totally dominated". LINKS Eric Weisstein's World of Mathematics, Crossed Prism Graph Eric Weisstein's World of Mathematics, Total Dominating Set Eric Weisstein's World of Mathematics, Well-Covered Graph Index entries for linear recurrences with constant coefficients, signature (5,5,-1). FORMULA From Andrew Howroyd, Apr 16 2018: (Start) a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3). G.f.: 4*x*(1 + 4*x - x^2)/((1 + x)*(1 - 6*x + x^2)). a(n) = 4*A090390(n) = 4*A001333(n)^2. (End) a(n) = 2*(chebyshevT(n,3) + (-1)^n). - Eric W. Weisstein, Apr 17 2018 a(n) = 4*(-1)^n*chebyshevT(n,i)^2, where i is the imaginary unit. - Eric W. Weisstein, Apr 17 2018 MATHEMATICA Table[2 (ChebyshevT[n, 3] + (-1)^n), {n, 20}] Table[4 (-1)^n ChebyshevT[n, I]^2, {n, 20}] LinearRecurrence[{5, 5, -1}, {4, 36, 196}, 20] CoefficientList[Series[-4 (-1 - 4 x + x^2)/(1 - 5 x - 5 x^2 + x^3), {x, 0, 20}], x] PROG (PARI) Vec(4*(1 + 4*x - x^2)/((1 + x)*(1 - 6*x + x^2)) + O(x^30)) \\ Andrew Howroyd, Apr 16 2018 (PARI) a(n) = 2*(polchebyshev(n, 1, 3) + (-1)^n); \\ Michel Marcus, Apr 17 2018 CROSSREFS Cf. A001333, A090390, A287062, A291772, A302941. Sequence in context: A270084 A272222 A263420 * A220436 A144888 A291643 Adjacent sequences:  A302943 A302944 A302945 * A302947 A302948 A302949 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 June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)