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Search: id:A082160
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| A082160 |
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Deterministic completely defined acyclic automata with 3 inputs and n+1 transient labeled states including a unique state having all transitions to the absorbing state. |
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+0
4
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| 1, 7, 315, 45682, 15646589, 10567689552, 12503979423607, 23841011541867520, 68835375121428936153, 286850872894190847235840, 1660638682341609286358474579, 12947089879912710544534553836032
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This is the first column of the array A082172.
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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)=b_3(n) where b_3(0) := 1, b_3(n) := sum(binomial(n, i)*(-1)^(n-i-1)*((i+2)^3-1)^(n-i)*b_3(i), i=0..n-1), n>0.
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CROSSREFS
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Cf. A082159, A082158.
Sequence in context: A002437 A086215 A119163 this_sequence A109059 A002000 A092588
Adjacent sequences: A082157 A082158 A082159 this_sequence A082161 A082162 A082163
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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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