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Search: id:A082164
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| A082164 |
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Deterministic completely defined initially connected acyclic automata with 3 inputs and n+1 transient unlabeled states including a unique state having all transitions to the absorbing state. |
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+0
3
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| 1, 7, 133, 5362, 380093, 42258384, 6830081860, 1520132414241, 447309239576913, 168599289097947589, 79364534944804317166
(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_2(n,k) form the array A082172. 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) := d_3(n)/(n-1)! where d_3(n) := b_3(n, 1)-sum(binomial(n-1, j-1)*T_3(n-j, j+1)*d_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+1)^3-1)^(n-i)*T_3(i, k), i=0..n-1), n>0.
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CROSSREFS
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Cf. A082160, A082163, A082162.
Adjacent sequences: A082161 A082162 A082163 this_sequence A082165 A082166 A082167
Sequence in context: A051832 A103050 A110111 this_sequence A119670 A003374 A001533
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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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