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A347558 Number of minimum dominating sets in the n-ladder graph. 5
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Eric W. Weisstein, Sep 06 2021

STATUS

approved

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Last modified January 25 19:00 EST 2022. Contains 350572 sequences. (Running on oeis4.)