A286985 Number of connected dominating sets in the n-prism graph.

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

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: A201958 A351477 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