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A303148 Number of minimal total dominating sets in the n-pan graph.

%I A303148 #15 Jun 10 2025 11:28:49
%S A303148 1,1,3,2,4,8,6,6,13,18,20,28,37,45,65,91,111,144,200,264,346,464,609,
%T A303148 798,1072,1428,1873,2479,3297,4361,5779,7670,10140,13416,17806,23598,
%U A303148 31229,41374,54820,72600,96197,127465,168801,223587,296255,392460,519856
%N A303148 Number of minimal total dominating sets in the n-pan graph.
%C A303148 Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, Apr 19 2018
%H A303148 Andrew Howroyd, <a href="/A303148/b303148.txt">Table of n, a(n) for n = 1..200</a>
%H A303148 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalTotalDominatingSet.html">Minimal Total Dominating Set</a>.
%H A303148 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PanGraph.html">Pan Graph</a>.
%H A303148 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,1,1,0,-1,-1).
%F A303148 From _Andrew Howroyd_, Apr 19 2018: (Start)
%F A303148 a(n) = a(n-3) + a(n-4) + a(n-5) + a(n-6) - a(n-8) - a(n-9) for n > 9.
%F A303148 G.f.: x*(1 + x + 3*x^2 + x^3 + 2*x^4 + 3*x^5 - x^6 - 4*x^7 - 3*x^8)/((1 - x^2 - x^3)*(1 + x^2 - x^6)). (End)
%t A303148 LinearRecurrence[{0, 0, 1, 1, 1, 1, 0, -1, -1}, {1, 1, 3, 2, 4, 8, 6, 6, 13}, 20]
%t A303148 CoefficientList[Series[(1 + x + 3 x^2 + x^3 + 2 x^4 + 3 x^5 - x^6 - 4 x^7 - 3 x^8)/(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9), {x, 0, 20}], x]
%o A303148 (PARI) Vec((1 + x + 3*x^2 + x^3 + 2*x^4 + 3*x^5 - x^6 - 4*x^7 - 3*x^8)/((1 - x^2 - x^3)*(1 + x^2 - x^6)) + O(x^40)) \\ _Andrew Howroyd_, Apr 19 2018
%Y A303148 Cf. A290273, A302506, A347650.
%K A303148 nonn,easy
%O A303148 1,3
%A A303148 _Eric W. Weisstein_, Apr 19 2018
%E A303148 a(1)-a(2) and terms a(20) and beyond from _Andrew Howroyd_, Apr 19 2018