A302760 Number of total dominating sets in the n-antiprism graph.

3, 11, 54, 179, 648, 2414, 8809, 32195, 117945, 431696, 1579955, 5783294, 21168592, 77482521, 283608249, 1038086883, 3799689944, 13907938601, 50906985592, 186333942984, 682034858839, 2496440225499, 9137676323347, 33446476209566, 122423549667123

Offset

1,1

Comments

Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, Apr 14 2018

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (3,1,6,-3,0,0,1).

Formula

From Andrew Howroyd, Apr 14 2018: (Start)

a(n) = 3*a(n-1) + a(n-2) + 6*a(n-3) - 3*a(n-4) + a(n-7) for n > 7.

G.f.: x*(3 + 2*x + 18*x^2 - 12*x^3 + 7*x^6)/(1 - 3*x - x^2 - 6*x^3 + 3*x^4 - x^7).

(End)

Mathematica

CoefficientList[Series[(3 + 2 x + 18 x^2 - 12 x^3 + 7 x^6)/(1 - 3 x - x^2 - 6 x^3 + 3 x^4 - x^7), {x, 0, 24}], x] (* Michael De Vlieger, Apr 14 2018 *)
LinearRecurrence[{3, 1, 6, -3, 0, 0, 1}, {3, 11, 54, 179, 648, 2414, 8809}, 20] (* Vincenzo Librandi, Apr 15 2018 *)
Table[RootSum[-1 + 3 #^3 - 6 #^4 - #^5 - 3 #^6 + #^7 &, #^n &], {n, 30}] (* Eric W. Weisstein, Apr 16 2018 *)
RootSum[-1 + 3 #^3 - 6 #^4 - #^5 - 3 #^6 + #^7 &, #^Range[30] &] (* Eric W. Weisstein, Apr 16 2018 *)

Prog

(PARI) Vec((3 + 2*x + 18*x^2 - 12*x^3 + 7*x^6)/(1 - 3*x - x^2 - 6*x^3 + 3*x^4 - x^7) + O(x^25)) \\ Andrew Howroyd, Apr 14 2018
(Magma) I:=[3, 11, 54, 179, 648, 2414, 8809]; [n le 7 select I[n] else 3*Self(n-1)+Self(n-2)+6*Self(n-3)-3*Self(n-4)+Self(n-7): n in [1..30]]; // Vincenzo Librandi, Apr 15 2018

Crossrefs

Cf. A302255, A302652, A302763.

Sequence in context: A129093 A259106 A057325 * A054700 A009280 A267832

Adjacent sequences: A302757 A302758 A302759 * A302761 A302762 A302763

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 12 2018

Extensions

a(1)-a(2) and terms a(11) and beyond from Andrew Howroyd, Apr 14 2018

Status

approved