A298823 Number of minimal total dominating sets in the n-dipyramidal graph.

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

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: A359817 A175041 A352342 * 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