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A286985 Number of connected dominating sets in the n-prism graph. 1
7, 7, 39, 115, 343, 967, 2663, 7203, 19239, 50887, 133543, 348179, 902775, 2329607, 5986535, 15327555, 39115847, 99532423, 252601127, 639548595, 1615746455, 4073951559, 10253517671, 25763632995, 64635943783, 161928486727, 405134009511, 1012371656275 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence extrapolated to a(1) and a(2) using recurrence. - Andrew Howroyd, Sep 04 2017

LINKS

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

Eric Weisstein's World of Mathematics, Connected Dominating Set

Eric Weisstein's World of Mathematics, Prism Graph

Index entries for linear recurrences with constant coefficients, signature (6, -11, 4, 5, -2, -1).

FORMULA

From Andrew Howroyd, Sep 04 2017: (Start)

a(n) = 6*a(n-1) - 11*a(n-2) + 4*a(n-3) + 5*a(n-4) - 2*a(n-5) - a(n-6) for n > 6.

G.f.: x*(7 - 35*x + 74*x^2 - 70*x^3 + 19*x^4 - 3*x^5)/((1 - x)^2*(1 - 2*x - x^2)^2).

(End)

MATHEMATICA

Rest @ CoefficientList[Series[x (7 - 35 x + 74 x^2 - 70 x^3 + 19 x^4 - 3 x^5)/((1 - x)^2*(1 - 2 x - x^2)^2), {x, 0, 28}], x] (* Michael De Vlieger, Sep 04 2017 *)

Table[LucasL[n, 2] + 2 n (3 Fibonacci[n - 2, 2] + Fibonacci[n - 1, 2] - 1) + 1, {n, 20}] (* Eric W. Weisstein, Sep 08 2017 *)

LinearRecurrence[{6, -11, 4, 5, -2, -1}, {7, 7, 39, 115, 343, 967}, 20] (* Eric W. Weisstein, Sep 08 2017 *)

PROG

(PARI) Vec((7 - 35*x + 74*x^2 - 70*x^3 + 19*x^4 - 3*x^5)/((1 - x)^2*(1 - 2*x - x^2)^2) + O(x^30))

CROSSREFS

Cf. A284702, A286182.

Sequence in context: A112685 A201958 A153721 * A151791 A022667 A143430

Adjacent sequences:  A286982 A286983 A286984 * A286986 A286987 A286988

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, May 17 2017

EXTENSIONS

a(1)-a(2) and terms a(14) and beyond from Andrew Howroyd, Sep 04 2017

STATUS

approved

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Last modified October 21 08:42 EDT 2018. Contains 316405 sequences. (Running on oeis4.)