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%I #16 Oct 08 2022 22:21:03
%S 2,12,30,74,200,522,1362,3572,9350,24474,64080,167762,439202,1149852,
%T 3010350,7881194,20633240,54018522,141422322,370248452,969323030,
%U 2537720634,6643838880,17393796002,45537549122,119218851372,312119004990,817138163594,2139295485800
%N Number of odd chordless cycles in the (2n+1)-prism graph.
%C Sequence extended to a(1) using the formula/recurrence (actual count for the 3-prism is 0, which reproduces A301775).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChordlessCycle.html">Chordless Cycle</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, 2, -1).
%F a(n) = A002878(n) + A131713(n).
%F a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4).
%F G.f.: -2*x*(1+x)*(x^2-3*x-1) / ( (1+x+x^2)*(x^2-3*x+1) ).
%t Table[LucasL[2 n + 1] + 2 Cos[(2 n + 1) Pi/3], {n, 20}]
%t LinearRecurrence[{2, 1, 2, -1}, {2, 12, 30, 74}, 20]
%t CoefficientList[Series[-2 (-1 - 4 x - 2 x^2 + x^3)/(1 - 2 x - x^2 - 2 x^3 + x^4), {x, 0, 20}], x]
%Y Cf. A002878, A131713, A301775.
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Mar 26 2018