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%I #19 May 02 2023 14:58:35
%S 9,13,49,129,361,989,2689,7233,19273,50925,133585,348225,902825,
%T 2329661,5986593,15327617,39115913,99532493,252601201,639548673,
%U 1615746537,4073951645,10253517761,25763633089,64635943881,161928486829,405134009617,1012371656385
%N Number of connected dominating sets on the n-Moebius ladder.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,4,5,-2,-1).
%F a(n) = (1 - 5*n)*LucasL(n, 2) + 2*(8*Fibonacci(n, 2) + 1)*n - 1.
%F a(n) = 6*a(n-1) - 11*a(n-2) + 4*a(n-3) + 5*a(n-4) - 2*a(n-5) - a(n-6).
%F G.f.: -x*(-9+41*x-70*x^2+58*x^3-29*x^4+x^5)/((-1+x)^2*(-1+2*x+x^2)^2).
%t Table[(1 - 5 n) LucasL[n, 2] + 2 (8 Fibonacci[n, 2] + 1) n - 1, {n, 20}]
%t Table[-1 + (1 - Sqrt[2])^n + (1 + Sqrt[2])^n + (2 + (1 + Sqrt[2])^n (-5 + 4 Sqrt[2]) - (1 - Sqrt[2])^n (5 + 4 Sqrt[2])) n, {n, 20}] // Expand
%t CoefficientList[Series[-((-9 + 41 x - 70 x^2 + 58 x^3 - 29 x^4 + x^5)/((-1 + x)^2 (-1 + 2 x + x^2)^2)), {x, 0, 20}], x]
%t LinearRecurrence[{6, -11, 4, 5, -2, -1}, {9, 13, 49, 129, 361, 989}, 20]
%K nonn
%O 1,1
%A _Eric W. Weisstein_, May 17 2017
%E a(13) from _Eric W. Weisstein_, Jun 30 2017
%E a(1), a(2) and a(14) and above from _Eric W. Weisstein_, Dec 02 2022
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