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

%I A347558 #14 Feb 16 2025 08:34:02
%S A347558 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,
%T A347558 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,
%U A347558 2,116,2,120,2,124,2,128,2,132,2,136,2,140,2,144,2
%N A347558 Number of minimum dominating sets in the n-ladder graph.
%H A347558 Andrew Howroyd, <a href="/A347558/b347558.txt">Table of n, a(n) for n = 1..1000</a>
%H A347558 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>
%H A347558 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>
%H A347558 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A347558 a(n) = 2*(n+2) for mod(n, 2)=0 and n != 2,6.
%F A347558 a(n) = 2 for mod(n, 2)=1 and n != 3.
%F A347558 a(n) = 2*a(n-2)-a(n-4) for n > 6.
%F A347558 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).
%t A347558 Join[{2, 6, 3, 12, 2, 17}, LinearRecurrence[{0, 2, 0, -1}, {2, 20, 2, 24}, 20]]
%t A347558 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]
%o A347558 (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
%Y A347558 Row 2 of A350820.
%Y A347558 Cf. A347634.
%K A347558 nonn,easy
%O A347558 1,1
%A A347558 _Eric W. Weisstein_, Sep 06 2021