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%I #23 Mar 04 2024 00:00:42
%S 3,4,7,6,6,15,15,22,28,45,58,79,115,159,223,307,438,609,852,1194,1675,
%T 2347,3282,4606,6451,9040,12663,17749,24871,34845,48831,68424,95883,
%U 134350,188266,263811,369667,518002,725860,1017129,1425262,1997179,2798583
%N Number of minimal dominating sets in the n-wheel graph.
%C The n-wheel graph is well defined for n >= 4. If the sequence is extended to n=1 using A253413 then the initial terms are 1,2,3,4,... If the sequence is extended using the recurrence the initial terms are 7,1,3,4,... - _Andrew Howroyd_, Jul 27 2017
%H Vincenzo Librandi, <a href="/A290270/b290270.txt">Table of n, a(n) for n = 3..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -1, -1, 1).
%F From _Andrew Howroyd_, Jul 27 2017: (Start)
%F a(n) = A253413(n-1) + 1 for n > 2.
%F a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-6) - 1 for n>8.
%F G.f.: x*(7 - 6*x - 5*x^2 + 2*x^5 + x^6) / ((1 - x^2 - x^3 -x^4 + x^6)*(1 - x)).
%F (End)
%F G.f.: x^3*(3+x-5*x^3-7*x^4+6*x^5+x^6)/((1-x^2-x^3-x^4+x^6)*(1-x)). - _Vincenzo Librandi_, Aug 04 2017
%t Table[1 + RootSum[1 - #1^2 - #1^3 - #1^4 + #1^6 &, #^(n - 1) &], {n, 3, 20}] (* _Eric W. Weisstein_, Aug 04 2017 *)
%t LinearRecurrence[{1, 1, 0, 0, -1, -1, 1}, {3, 4, 7, 6, 6, 15, 15}, 20] (* _Eric W. Weisstein_, Aug 04 2017 *)
%t CoefficientList[Series[(3 + x - 5 x^3 - 7 x^4 + 6 x^5 + x^6)/((1 - x^2 - x^3 - x^4 + x^6) (1-x)), {x, 0,33}], x] (* _Vincenzo Librandi_, Aug 04 2017 *)
%o (PARI)
%o Vec(((7-6*x-5*x^2+2*x^5+x^6)) / ((1-x^2-x^3-x^4+x^6)*(1-x)) + O(x^40)) \\ _Andrew Howroyd_, Jul 27 2017
%o (Magma) I:=[3,4,7,6,6,15,15,22,28]; [n le 9 select I[n] else Self(n-2)+Self(n-3)+Self(n-4)-Self(n-6)-1: n in [1..50]]; // _Vincenzo Librandi_, Aug 04 2017
%Y Cf. A253413.
%K nonn
%O 3,1
%A _Eric W. Weisstein_, Jul 25 2017
%E a(3) and a(16)-a(45) from _Andrew Howroyd_, Jul 27 2017
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