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 A298823 Number of minimal total dominating sets in the n-dipyramidal graph. 1
 2, 4, 9, 12, 15, 21, 21, 20, 30, 45, 44, 49, 65, 77, 98, 132, 153, 180, 247, 329, 409, 528, 690, 889, 1180, 1573, 2037, 2657, 3538, 4684, 6169, 8164, 10783, 14229, 18877, 25036, 33078, 43757, 57996, 76809, 101721, 134773, 178450, 236284, 313097, 414828, 549383 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 Eric Weisstein's World of Mathematics, Dipyramidal Graph Eric Weisstein's World of Mathematics, Total Dominating Set Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1,0,0,-1,0,1,1,-1). FORMULA From Andrew Howroyd, Jun 26 2018: (Start) a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) - a(n-7) + a(n-9) + a(n-10) - a(n-11) for n > 11. G.f.: x*(2 + 3*x^2 - 4*x^3 - 2*x^4 - 2*x^5 - 9*x^6 - 2*x^7 + 9*x^8 + 12*x^9 - 9*x^10)/((1 - x)^2*(1 - x^2 - x^3)*(1 + x^2 - x^6)). (End) MATHEMATICA Table[2 n + RootSum[-1 - # + #^3 &, #^n &] + (1 + (-1)^n) RootSum[-1 - # + #^3 &, #^(-n/2) &], {n, 20}] LinearRecurrence[{2, -1, 1, -1, 0, 0, -1, 0, 1, 1, -1}, {2, 4, 9, 12, 15, 21, 21, 20, 30, 45, 44}, 20] CoefficientList[Series[(2 + 3 x^2 - 4 x^3 - 2 x^4 - 2 x^5 - 9 x^6 - 2 x^7 + 9 x^8 + 12 x^9 - 9 x^10)/((-1 + x)^2 (1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)), {x, 0, 20}], x] PROG (PARI) Vec((2 + 3*x^2 - 4*x^3 - 2*x^4 - 2*x^5 - 9*x^6 - 2*x^7 + 9*x^8 + 12*x^9 - 9*x^10)/((1 - x)^2*(1 - x^2 - x^3)*(1 + x^2 - x^6)) + O(x^50)) \\ Andrew Howroyd, Jun 26 2018 CROSSREFS Sequence in context: A022428 A096186 A175041 * A219114 A182859 A341239 Adjacent sequences:  A298820 A298821 A298822 * A298824 A298825 A298826 KEYWORD nonn AUTHOR Eric W. Weisstein, Jun 18 2018 EXTENSIONS a(1)-a(2) and terms a(21) and beyond from Andrew Howroyd, Jun 26 2018 STATUS approved

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Last modified July 29 05:30 EDT 2021. Contains 346340 sequences. (Running on oeis4.)