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%I #23 Sep 09 2017 07:54:59
%S 7,7,39,115,343,967,2663,7203,19239,50887,133543,348179,902775,
%T 2329607,5986535,15327555,39115847,99532423,252601127,639548595,
%U 1615746455,4073951559,10253517671,25763632995,64635943783,161928486727,405134009511,1012371656275
%N Number of connected dominating sets in the n-prism graph.
%C Sequence extrapolated to a(1) and a(2) using recurrence. - _Andrew Howroyd_, Sep 04 2017
%H Andrew Howroyd, <a href="/A286985/b286985.txt">Table of n, a(n) for n = 1..200</a>
%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/PrismGraph.html">Prism Graph</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 From _Andrew Howroyd_, Sep 04 2017: (Start)
%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) for n > 6.
%F G.f.: x*(7 - 35*x + 74*x^2 - 70*x^3 + 19*x^4 - 3*x^5)/((1 - x)^2*(1 - 2*x - x^2)^2).
%F (End)
%t Rest @ CoefficientList[Series[x (7 - 35 x + 74 x^2 - 70 x^3 + 19 x^4 - 3 x^5)/((1 - x)^2*(1 - 2 x - x^2)^2), {x, 0, 28}], x] (* _Michael De Vlieger_, Sep 04 2017 *)
%t Table[LucasL[n, 2] + 2 n (3 Fibonacci[n - 2, 2] + Fibonacci[n - 1, 2] - 1) + 1, {n, 20}] (* _Eric W. Weisstein_, Sep 08 2017 *)
%t LinearRecurrence[{6, -11, 4, 5, -2, -1}, {7, 7, 39, 115, 343, 967}, 20] (* _Eric W. Weisstein_, Sep 08 2017 *)
%o (PARI) Vec((7 - 35*x + 74*x^2 - 70*x^3 + 19*x^4 - 3*x^5)/((1 - x)^2*(1 - 2*x - x^2)^2) + O(x^30))
%Y Cf. A284702, A286182.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, May 17 2017
%E a(1)-a(2) and terms a(14) and beyond from _Andrew Howroyd_, Sep 04 2017
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