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
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).
Programs
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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).