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

Author

Eric W. Weisstein, Sep 06 2021

Keywords

• nonn
• easy

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).

Crossrefs

Row 2 of A350820.

Cf. A347634.

Programs

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]

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

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).