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A284700 Number of edge covers in the n-antiprism graph.

%I A284700 #15 Feb 16 2025 08:33:43
%S A284700 4,13,205,2902,41413,590758,8427370,120219259,1714968133,24464596729,
%T A284700 348995693650,4978540849669,71020558255594,1013132129923498,
%U A284700 14452670295681235,206172198577335937,2941115696724530533,41956003773586931038,598516493115066264085
%N A284700 Number of edge covers in the n-antiprism graph.
%C A284700 Sequence extrapolated to n=0 using recurrence. - _Andrew Howroyd_, May 15 2017
%H A284700 G. C. Greubel, <a href="/A284700/b284700.txt">Table of n, a(n) for n = 0..860</a> (terms 0..200 from Andrew Howroyd)
%H A284700 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>
%H A284700 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>
%H A284700 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (13,18,1,-4).
%F A284700 From _Andrew Howroyd_, May 15 2017 (Start)
%F A284700 a(n) = 13*a(n-1)+18*a(n-2)+a(n-3)-4*a(n-4) for n>=4.
%F A284700 G.f.: (-x^3-36*x^2-39*x+4)/(4*x^4-x^3-18*x^2-13*x+1).
%F A284700 (End)
%t A284700 Table[RootSum[4 - # - 18 #^2 - 13 #^3 + #^4 &, #^n &], {n, 0, 20}] (* _Eric W. Weisstein_, May 17 2017 *)
%t A284700 LinearRecurrence[{13, 18, 1, -4}, {13, 205, 2902, 41413}, {0, 20}] (* _Eric W. Weisstein_, May 17 2017 *)
%t A284700 CoefficientList[Series[(-x^3-36*x^2-39*x+4)/(4*x^4-x^3-18*x^2-13*x+1), {x, 0, 50}], x]
%o A284700 (PARI)
%o A284700 Vec((-x^3-36*x^2-39*x+4)/(4*x^4-x^3-18*x^2-13*x+1)+O(x^20)) \\ _Andrew Howroyd_, May 15 2017
%Y A284700 Cf. A123304, A020866, A192742, A286910, A284699.
%K A284700 nonn
%O A284700 0,1
%A A284700 _Eric W. Weisstein_, Apr 01 2017
%E A284700 a(0)-a(2) and a(9)-a(18) from _Andrew Howroyd_, May 15 2017