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%I #18 May 20 2022 02:47:35
%S 0,6,90,1050,11130,112266,1099098,10550826,99899514,936435786,
%T 8711707290,80572452714,741766408890,6803700252810,62219207836890,
%U 567597206875050,5167463468534010,46965976868507850,426262280218695450,3864157168469020650,34994228358927126330
%N Number of Condorcet voting profiles with three candidates and 2n-1 voters where all the choices are from {123, 231, 312}.
%C All terms are multiples of 6.
%H Shalosh B. Ekhad, <a href="https://sites.math.rutgers.edu/~zeilberg/tokhniot/oCondorcet3d.txt">More terms</a>.
%H Rebecca Embar and Doron Zeilberger, <a href="https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/cond3.pdf">Counting Condorcet</a>.
%F a(n) = ((17*n-21)*a(n-1)-(72*n-108)*a(n-2))/(n-1), with a(1) = 0, a(2) = 6.
%t Table[FullSimplify[3^(2*n - 1) - 2^(n-1) * Binomial[2*n, n] * Hypergeometric2F1[1, n + 1/2, n + 1, 8/9]/3], {n, 1, 25}] (* _Vaclav Kotesovec_, May 20 2022 *)
%Y Cf. A353194.
%K nonn
%O 1,2
%A _Rebecca Embar_, May 01 2022
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