A360876 Number of connected dominating sets in the 2 X n rook graph.

3, 9, 39, 177, 783, 3369, 14199, 58977, 242463, 989529, 4017159, 16245777, 65514543, 263652489, 1059392919, 4251920577, 17050729023, 68332056249, 273715645479, 1096024843377, 4387586157903, 17560804984809, 70274600998839, 281192547174177, 1125052618233183

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Formula

a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) for n > 3.

G.f.: 3*x*(1 - 5*x + 8*x^2)/((1 - x)*(1 - 3*x)*(1 - 4*x)).

Mathematica

LinearRecurrence[{8, -19, 12}, {3, 9, 39}, 30] (* Paolo Xausa, Oct 03 2024 *)

Prog

(PARI) Vec(3*(1 - 5*x + 8*x^2)/((1 - x)*(1 - 3*x)*(1 - 4*x)) + O(x^25))

Crossrefs

Row 2 of A360875.

Cf. A360874.

Sequence in context: A180741 A121101 A280066 * A287063 A080635 A278749

Adjacent sequences: A360873 A360874 A360875 * A360877 A360878 A360879

Keyword

nonn,easy

Author

Andrew Howroyd, Feb 24 2023

Status

approved