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A302760 Number of total dominating sets in the n-antiprism graph. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)