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%I A123304 #24 Feb 16 2025 08:33:02
%S A123304 4,5,43,263,1699,10895,69943,448943,2881699,18497135,118730023,
%T A123304 762108143,4891844659,31399932335,201550911703,1293721577903,
%U A123304 8304182337859,53303156937455,342144045482503,2196165379031663,14096818096762579,90485116626705455,580808823292457143
%N A123304 Number of edge covers for the circular ladder (n-prism graph) C_n X K_2.
%C A123304 An edge covering for a graph is a set of edges so that every vertex is adjacent to at least one edge of this set.
%C A123304 The number of edge coverings for the circle C_n for n>0 is the n-th Lucas number.
%H A123304 R. Tauraso, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Tauraso/tauraso18.html">Edge cover time for regular graphs</a>, JIS 11 (2008) 08.4.4
%H A123304 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>
%H A123304 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H A123304 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,9,1,-2).
%F A123304 a(n) = 5*a(n-1) +9*a(n-2) +a(n-3) -2*a(n-4).
%F A123304 G.f.: (4-15*x-18*x^2-x^3) / ((1+x)*(1-6*x-3*x^2+2*x^3)).
%t A123304 a[0] = 4; a[1] = 5; a[2] = 43; a[3] = 263; a[n_] := a[n] = 5a[n - 1] + 9a[n - 2] + a[n - 3] - 2a[n - 4]; Table[a[n], {n, 0, 19}] (* _Robert G. Wilson v_, Sep 26 2006 *)
%t A123304 CoefficientList[ Series[(4 - 15x - 18x^2 - x^3)/((1 + x)*(1 - 6x - 3x^2 + 2x^3)), {x, 0, 19}], x] (* _Robert G. Wilson v_, Sep 26 2006 *)
%t A123304 Table[(-1)^n + RootSum[2 - 3 # - 6 #^2 + #^3 &, #^n &], {n, 0, 20}] (* _Eric W. Weisstein_, Mar 29 2017 *)
%t A123304 LinearRecurrence[{5, 9, 1, -2}, {5, 43, 263, 1699}, {0, 20}] (* _Eric W. Weisstein_, Aug 09 2017 *)
%o A123304 (PARI) x='x+O('x^99); Vec((4-15*x-18*x^2-x^3)/((1+x)*(1-6*x-3*x^2+2*x^3))) \\ _Altug Alkan_, Aug 10 2017
%K A123304 nonn,easy,changed
%O A123304 0,1
%A A123304 _Roberto Tauraso_, Sep 24 2006

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