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Search: id:A082158
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| A082158 |
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Number of deterministic completely defined acyclic automata with 3 inputs and n transient labeled states (and a unique absorbing state). |
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+0
4
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| 1, 1, 15, 1024, 198581, 85102056, 68999174203, 95264160938080, 207601975572545961, 674354204416939196800, 3122476748685067008205511, 19884561572783089348189507584
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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This is the first column of the array A082170.
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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)=a_3(n) where a_3(0) := 1, a_3(n) := sum(binomial(n, i)*(-1)^(n-i-1)*(i+1)^(3*n-3*i)*a_3(i), i=0..n-1), n>0.
1 = Sum_{n>=0} a(n)*exp(-(1+n)^3*x)*x^n/n!. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 18 2005
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CROSSREFS
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Cf. A082157.
Sequence in context: A067408 A102102 A019282 this_sequence A064625 A131313 A129764
Adjacent sequences: A082155 A082156 A082157 this_sequence A082159 A082160 A082161
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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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