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%I #12 Mar 16 2022 02:58:20
%S 0,1,4,3,14,5,30,7,52,9,80,11,114,13,154,15,200,17,252,19,310,21,374,
%T 23,444,25,520,27,602,29,690,31,784,33,884,35,990,37,1102,39,1220,41,
%U 1344,43,1474,45,1610,47,1752,49,1900,51,2054,53,2214,55,2380,57,2552,59,2730
%N Number of minimum edge covers in the n-vertex wheel graph.
%C The wheel graph is well defined on n >= 4 vertices; sequence extended to n = 1 using the formulas/generating function.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimumEdgeCover.html">Minimum Edge Cover</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_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F a(n) = n - 1 for n == 0 (mod 2).
%F a(n) = (n - 1)*(3*n + 1)/4 for n == 1 (mod 2).
%F a(n) = (3*n^2 + 2*n - 3*(-1)^n*(n - 1)^2 - 5)/8.
%F G.f.: x^2*(-1 - 5*x - x^3 + x^4)/(-1 + x^2)^3.
%F E.g.f.: (4 + (x - 4)*cosh(x) + (3*x^2 + 4*x - 1)*sinh(x))/4. - _Stefano Spezia_, Mar 15 2022
%t Table[Piecewise[{{n - 1, Mod[n, 2] == 0}, {(n - 1) (3 n + 1)/4, Mod[n, 2] == 1}}, 0], {n, 20}]
%t LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 1, 5, 3, 16, 5}, 20]
%t Table[(3 n^2 + 2 n - 3 (-1)^n (n - 1)^2 - 5)/8, {n, 20}]
%t CoefficientList[Series[x (-1 - 5 x - x^3 + x^4)/(-1 + x^2)^3, {x, 0, 20}], x]
%K nonn,easy
%O 1,3
%A _Eric W. Weisstein_, Feb 27 2022