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A284702 Number of dominating sets in the n-prism graph.

%I A284702 #30 Feb 16 2025 08:33:43
%S A284702 3,11,51,183,663,2435,8935,32775,120219,440971,1617531,5933271,
%T A284702 21763823,79831875,292831311,1074134535,3940032883,14452434635,
%U A284702 53012975555,194456895863,713287340551,2616409296963,9597250953527,35203676264199,129130605057163
%N A284702 Number of dominating sets in the n-prism graph.
%C A284702 Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, May 10 2017
%H A284702 G. C. Greubel, <a href="/A284702/b284702.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..200 from Andrew Howroyd)
%H A284702 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>
%H A284702 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H A284702 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,5,1,1,-1,-1).
%F A284702 From _Andrew Howroyd_, May 10 2017: (Start)
%F A284702 a(n) = 3*a(n-1) + a(n-2) + 5*a(n-3) + a(n-4) + a(n-5) - a(n-6) - a(n-7).
%F A284702 G.f.: x*(-7*x^6 - 6*x^5 + 5*x^4 + 4*x^3 + 15*x^2 + 2*x + 3)/((x^2 + 1)*(x^5 + x^4 - 2*x^3 - 2*x^2 - 3*x + 1)). (End)
%t A284702 LinearRecurrence[{3, 1, 5, 1, 1, -1, -1}, {3, 11, 51, 183, 663, 2435,
%t A284702   8935}, 20] (* _Eric W. Weisstein_, May 17 2017 *)
%t A284702 Rest[CoefficientList[Series[x (-7 x^6 - 6 x^5 + 5 x^4 + 4 x^3 + 15 x^2 + 2 x + 3)/((x^2 + 1) (x^5 + x^4 - 2 x^3 - 2 x^2 - 3 x + 1)), {x, 0, 20}], x]] (* _G. C. Greubel_, May 17 2017 *)
%t A284702 Table[2 Cos[n Pi/2] + RootSum[1 + #1 - 2 #1^2 - 2 #1^3 - 3 #1^4 + #1^5 &, #^n &], {n, 20}] (* _Eric W. Weisstein_, May 26 2017 *)
%o A284702 (PARI)
%o A284702 Vec((-7*x^6-6*x^5+5*x^4+4*x^3+15*x^2+2*x+3)/((x^2+1)*(x^5+x^4-2*x^3-2*x^2-3*x+1))+O(x^15)) \\ _Andrew Howroyd_, May 10 2017
%Y A284702 Cf. A051927, A102080, A284699, A218348 (ladder), A284663.
%K A284702 nonn,easy
%O A284702 1,1
%A A284702 _Eric W. Weisstein_, Apr 01 2017
%E A284702 a(1)-a(2) and a(16)-a(25) from _Andrew Howroyd_, May 10 2017