A353230 Number of Condorcet voting profiles with three candidates and 2n-1 voters where all the choices are from {123, 231, 312}.

0, 6, 90, 1050, 11130, 112266, 1099098, 10550826, 99899514, 936435786, 8711707290, 80572452714, 741766408890, 6803700252810, 62219207836890, 567597206875050, 5167463468534010, 46965976868507850, 426262280218695450, 3864157168469020650, 34994228358927126330

Offset: 1

Author

Rebecca Embar, May 01 2022

Keywords

• nonn

Comments

All terms are multiples of 6.

Links

• Shalosh B. Ekhad, More terms.
• Rebecca Embar and Doron Zeilberger, Counting Condorcet.

Crossrefs

Cf. A353194.

Programs

Mathematica

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 *)

Formula

a(n) = ((17*n-21)*a(n-1)-(72*n-108)*a(n-2))/(n-1), with a(1) = 0, a(2) = 6.