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%I #6 Dec 08 2021 11:20:51
%S 3,7,10,15,16,18,29,31,40,48,67,82,105,143,189,255,341,474,647,892,
%T 1236,1719,2393,3330,4656,6503,9094,12719,17807,24931,34907,48895,
%U 68490,95951,134420,188338,263885,369743,518080,725940,1017211,1425346,1997265,2798671
%N Number of minimal dominating sets in the n-dipyramidal graph (for n > 3).
%C The 3-dipyramidal graph deviates from this sequence because it has 4 minimal dominating sets while a(3) = 10.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,0,-1,0,2,-1).
%F a(n) = A253413(n)+2*n+1.
%F a(n) = 2*a(n-1)-a(n-3)-a(n-5)+2*a(n-7)-a(n-8).
%F G.f.: x*(3+x-4*x^2-2*x^3-7*x^4-x^5+15*x^6-7*x^7))/((-1+x)^2*(1-x^2-x^3-x^4+x^6)).
%t Table[2 n + 1 + RootSum[1 - #^2 - #^3 - #^4 + #^6 &, #^n &], {n, 20}]
%t LinearRecurrence[{2, 0, -1, 0, -1, 0, 2, -1}, {3, 7, 10, 15, 16, 18, 29, 31}, 20]
%t CoefficientList[Series[(3 + x - 4 x^2 - 2 x^3 - 7 x^4 - x^5 + 15 x^6 - 7 x^7)/((-1 + x)^2 (1 - x^2 - x^3 - x^4 + x^6)), {x, 0, 20}], x]
%Y Cf. A253413.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Sep 09 2021