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A290336 Number of minimal dominating sets in the n-prism graph.

%I A290336 #18 Feb 16 2025 08:33:49
%S A290336 11,12,37,55,149,316,596,1219,2444,4971,10103,20465,41746,84924,
%T A290336 172501,350668,712597,1448447,2943959,5983344,12162310,24720787,
%U A290336 50246512,102129655,207584129,421928981,857596064,1743117100,3543000201,7201373724,14637255611
%N A290336 Number of minimal dominating sets in the n-prism graph.
%C A290336 The prism graphs are defined for n>=3. If the sequence is extended to n=1 using P_n X P_2 then a(1)=2 and a(2)=6 (as A290379). The empirical recurrence is the same as that for the Moebius ladder graph (see A290337). - _Andrew Howroyd_, Aug 01 2017
%H A290336 Andrew Howroyd, <a href="/A290336/b290336.txt">Table of n, a(n) for n = 3..200</a>
%H A290336 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>
%H A290336 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%F A290336 Empirical: a(n) = a(n-1)+a(n-2)+2*a(n-3) -a(n-4)+2*a(n-5)-2*a(n-6) +6*a(n-7)+4*a(n-8)+4*a(n-9) -6*a(n-10)-3*a(n-12) +5*a(n-13)-a(n-14)-2*a(n-15) -5*a(n-16)-2*a(n-17)-2*a(n-18) for n > 20. - _Andrew Howroyd_, Aug 01 2017
%F A290336 Empirical g.f.: x^3*(11 + x + 14*x^2 - 16*x^3 + 44*x^4 + 28*x^5 + 56*x^6 - 52*x^7 - 6*x^8 - 70*x^9 + 52*x^10 - 28*x^11 - 23*x^12 - 97*x^13 - 56*x^14 - 62*x^15 - 12*x^16 - 8*x^17) / ((1 - x)*(1 + 2*x^4 + x^6)*(1 - x^2 - 3*x^3 - 4*x^4 - 4*x^5 - x^6 - 2*x^7 - 3*x^8 - 5*x^9 - 4*x^10 - 2*x^11)). - _Colin Barker_, Aug 02 2017
%Y A290336 Cf. A284702, A290337, A290379.
%K A290336 nonn
%O A290336 3,1
%A A290336 _Eric W. Weisstein_, Jul 27 2017
%E A290336 Terms a(9) and beyond from _Andrew Howroyd_, Aug 01 2017