%I #9 Feb 16 2025 08:34:02

%S 17,81,405,2025,10125,50625,253125,1265625,6328125,31640625,158203125,

%T 791015625,3955078125,19775390625,98876953125,494384765625,

%U 2471923828125,12359619140625,61798095703125,308990478515625,1544952392578125,7724761962890625

%N Number of dominating sets in the n-alkane graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlkaneGraph.html">Alkane Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (5).

%F a(n) = 81*5^(n-2) for n > 1.

%F G.f.: x*(4*x - 17)/(5*x - 1).

%F E.g.f.: (81*exp(5*x) + 20*x - 81)/25. - _Stefano Spezia_, Sep 04 2021

%t Join[{17}, LinearRecurrence[{5}, {81}, 20]]

%t CoefficientList[Series[(4 x - 17)/(5 x - 1), {x, 0, 20}], x]

%Y Cf. A180148, A228602, A347478.

%K nonn,easy,changed

%O 1,1

%A _Eric W. Weisstein_, Sep 04 2021