%I #6 Sep 09 2021 16:20:58
%S 2,1,1,4,2,1,7,3,1,11,4,1,16,5,1,22,6,1,29,7,1,37,8,1,46,9,1,56,10,1,
%T 67,11,1,79,12,1,92,13,1,106,14,1,121,15,1,137,16,1,154,17,1,172,18,1,
%U 191,19,1,211,20,1,232,21,1,254,22,1,277,23,1,301,24
%N Number of minimum dominating sets in the n-pan graph (for n > 2).
%C Sequence extended to a(1) using the formula/recurrence.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PanGraph.html">Pan Graph</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,3,0,0,-3,0,0,1).
%F a(n) = 1 for n = 0 (mod 3)
%F (n^2+7*n+28)/18 for n = 1 (mod 3)
%F (n+1)/3 for n = 2 (mod 3).
%F a(n) = 3*a(n-3)-3*a(n-6)+a(n-9) for n>9.
%F G.f.: -x*(2 + x + x^2 - 2*x^3 - x^4 - 2*x^5 + x^6 + x^8)/((-1 + x)^3*(1 + x + x^2)^3).
%t Table[Piecewise[{{1, Mod[n, 3] == 0}, {(28 + 7 n + n^2)/18, Mod[n, 3] == 1}, {(n + 1)/3, Mod[n, 3] == 2}}], {n, 20}]
%t LinearRecurrence[{0, 0, 3, 0, 0, -3, 0, 0, 1}, {2, 1, 1, 4, 2, 1, 7, 3, 1}, 20]
%t CoefficientList[Series[-(2 + x + x^2 - 2 x^3 - x^4 - 2 x^5 + x^6 + x^8)/((-1 + x)^3 (1 + x + x^2)^3), {x, 0, 20}], x]
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Sep 09 2021