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 A082159 Number of deterministic completely defined acyclic automata with 2 inputs and n+1 transient labeled states including a unique state having all transitions to the absorbing state. 3
 1, 3, 39, 1206, 69189, 6416568, 881032059, 168514815360, 42934911510249, 14081311783382400, 5786296490491543599, 2914663547018935095552, 1767539279001227299807725, 1271059349855055258673975296, 1069996840045068513065229943875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is the first column of the array A082171. LINKS 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)=b_2(n) where b_2(0) := 1, b_2(n) := sum(binomial(n, i)*(-1)^(n-i-1)*((i+2)^2-1)^(n-i)*b_2(i), i=0..n-1), n>0. MATHEMATICA a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, i] (-1)^(n - i - 1) ((i + 2)^2 - 1)^(n - i) a[i], {i, 0, n - 1}]; Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Aug 29 2019 *) CROSSREFS Cf. A082157, A082171. Sequence in context: A276964 A274573 A278750 * A187536 A084881 A193122 Adjacent sequences:  A082156 A082157 A082158 * A082160 A082161 A082162 KEYWORD easy,nonn AUTHOR Valery A. Liskovets, Apr 09 2003 STATUS approved

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)