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%I #6 Feb 25 2024 06:40:45
%S 0,2,0,2,8,2,24,16,48,92,100,310,344,808,1344,2102,4480,6462,13092,
%T 21662,37488,69904,113652,212844,359856,636402,1134068,1937072,
%U 3493120,6012746,10639264,18706394,32550976,57727738,100407848,177116816,310493720,543717148
%N Number of odd chordless cycles in the n-antiprism graph.
%C Sequence extended to a(0)-a(3) using the formula/recurrence (actual 3-antiprism count is 0).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChordlessCycle.html">Chordless Cycle</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2, 2, -1, 2, -1).
%F a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).
%F G.f.: 2*x*(1 - x^2 + 2*x^3)/( (x^3-x^2-2*x-1)*(x^3-x^2+2*x-1)).
%F 2*a(n) = -3*A077990(n) -4*A077990(n-1)-A077990(n-2) +3*A005314(n+1) -4*A005314(n)+A005314(n-1). - _R. J. Mathar_, Feb 25 2024
%t Table[(RootSum[-1 + #1 - 2 #1^2 + #1^3 &, #1^n &] - RootSum[-1 + #1 + 2 #1^2 + #1^3 &, #1^n &])/2, {n, 0, 20}]
%t LinearRecurrence[{0, 2, 2, -1, 2, -1}, {0, 2, 0, 2, 8, 2}, 20]
%t CoefficientList[Series[2 x (1 - x^2 + 2 x^3)/(1 - 2 x^2 - 2 x^3 + x^4 - 2 x^5 + x^6), {x, 0, 20}], x]
%K nonn,easy
%O 0,2
%A _Eric W. Weisstein_, Mar 26 2018
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