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Search: id:A082162
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| A082162 |
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Number of deterministic completely defined initially connected acyclic automata with 3 inputs and n transient unlabeled states (and a unique absorbing state). |
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12
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| 1, 7, 139, 5711, 408354, 45605881, 7390305396, 1647470410551, 485292763088275, 183049273155939442, 86211400693272461866
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Coefficients T_3(n,k) form the array A082170. These automata have no nontrivial automorphisms (by states).
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REFERENCES
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V. A. Liskovets, Exact enumeration of acyclic automata, Proc. 15th Conf. "Formal Power Series and Algebr. Combin. (FPSAC'03)", 2003.
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LINKS
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V. A. Liskovets, Exact enumeration of acyclic deterministic automata,Discrete Appl. Math., 154, No.3 (2006), 537-551.
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FORMULA
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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 (pauldhanna(AT)juno.com), Jan 07 2005
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CROSSREFS
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Cf. A082158, A082161.
Cf. A102098, A102400.
Adjacent sequences: A082159 A082160 A082161 this_sequence A082163 A082164 A082165
Sequence in context: A056254 A137463 A126156 this_sequence A085708 A054606 A070074
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KEYWORD
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easy,nonn
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AUTHOR
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Valery Liskovets (liskov(AT)im.bas-net.by), Apr 09 2003
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EXTENSIONS
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More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Jan 07 2005
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