A347558 Number of minimum dominating sets in the n-ladder graph.

2, 6, 3, 12, 2, 17, 2, 20, 2, 24, 2, 28, 2, 32, 2, 36, 2, 40, 2, 44, 2, 48, 2, 52, 2, 56, 2, 60, 2, 64, 2, 68, 2, 72, 2, 76, 2, 80, 2, 84, 2, 88, 2, 92, 2, 96, 2, 100, 2, 104, 2, 108, 2, 112, 2, 116, 2, 120, 2, 124, 2, 128, 2, 132, 2, 136, 2, 140, 2, 144, 2

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Ladder Graph

Eric Weisstein's World of Mathematics, Minimum Dominating Set

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Formula

a(n) = 2*(n+2) for mod(n, 2)=0 and n != 2,6.

a(n) = 2 for mod(n, 2)=1 and n != 3.

a(n) = 2*a(n-2)-a(n-4) for n > 6.

G.f.: x*(2 + 6*x - x^2 - 2*x^4 - x^5 + x^6 - 2*x^7 + x^9)/((-1 + x)^2*(1 + x)^2).

Mathematica

Join[{2, 6, 3, 12, 2, 17}, LinearRecurrence[{0, 2, 0, -1}, {2, 20, 2, 24}, 20]]
CoefficientList[Series[(2 + 6 x - x^2 - 2 x^4 - x^5 + x^6 - 2 x^7 + x^9)/((-1 + x)^2 (1 + x)^2), {x, 0, 20}], x]

Prog

(PARI) a(n)={if(n%2, 1, n+2)*2 + if(n<=6, [0, -2, 1, 0, 0, 1][n])} \\ Andrew Howroyd, Jan 18 2022

Crossrefs

Row 2 of A350820.

Cf. A347634.

Sequence in context: A079178 A322365 A297553 * A317490 A256466 A303771

Adjacent sequences: A347555 A347556 A347557 * A347559 A347560 A347561

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 06 2021

Status

approved