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 A082162 Number of deterministic completely defined initially connected acyclic automata with 3 inputs and n transient unlabeled states (and a unique absorbing state). 12
 1, 7, 139, 5711, 408354, 45605881, 7390305396, 1647470410551, 485292763088275, 183049273155939442, 86211400693272461866 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Coefficients T_3(n,k) form the array A082170. These automata have no nontrivial automorphisms (by states). REFERENCES R. Bacher, C. Reutenauer, The number of right ideals of given codimension over a finite field, in Noncommutative Birational Geometry, Representations and Combinatorics, edited by Arkady. Berenstein and Vladimir. Retakha, Contemporary Mathematics, Vol. 592, 2013. LINKS Vaclav Kotesovec (after Jean-François Alcover), Table of n, a(n) for n = 1..210 V. A. Liskovets, Exact enumeration of acyclic automata, Proc. 15th Conf. "Formal Power Series and Algebr. Combin. (FPSAC'03)", 2003. V. A. Liskovets, Exact enumeration of acyclic deterministic automata, Discrete Appl. Math., 154, No.3 (2006), 537-551. FORMULA a(n) = c_3(n)/(n-1)! where c_3(n) = T_3(n, 1) - sum(binomial(n-1, j-1)*T_3(n-j, j+1)*c_3(j), j=1..n-1) and T_3(0, k) = 1, T_3(n, k) = sum(binomial(n, i)*(-1)^(n-i-1)*(i+k)^(3*n-3*i)*T_3(i, k), i=0..n-1), n>0. Equals column 0 of triangle A102098. Also equals main diagonal of A102400: a(n) = A102098(n, 0) = A102400(n, n). - Paul D. Hanna, Jan 07 2005 MATHEMATICA T[n_, k_] := T[n, k] = If[n

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Last modified December 6 19:31 EST 2019. Contains 329809 sequences. (Running on oeis4.)