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 A082169 Deterministic completely defined quasi-acyclic automata with 2 inputs, n transient and k absorbing labeled states. 5
 1, 1, 1, 1, 4, 7, 1, 9, 56, 142, 1, 16, 207, 1780, 5941, 1, 25, 544, 9342, 103392, 428856, 1, 36, 1175, 32848, 709893, 9649124, 47885899, 1, 49, 2232, 91150, 3142528, 82305144, 1329514816, 7685040448, 1, 64, 3871, 215892, 10682325, 440535696, 13598786979, 254821480596, 1681740027657 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Array read by antidiagonals: (0,1),(0,2),(1,1),(0,3),... The first column is A082157. 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 T(n, k)=T_2(n, k) where T_2(0, k) := 1, T_2(n, k) := sum(binomial(n, i)*(-1)^(n-i-1)*(i+k)^(2*n-2*i)*T_2(i, k), i=0..n-1), n>0; EXAMPLE The array begins: 1 1 1 1 1 1 1 1 1 - k=0 1 4 9 16 25 36 49 64 81 - k=1 7 56 207 544 1175 2232 3871 6272 9639 - k=2 MATHEMATICA T[0, _] = 1; T[n_, k_] := T[n, k] = Sum[Binomial[n, i] (-1)^(n - i - 1)*(i + k)^(2n - 2i) T[i, k], {i, 0, n - 1}]; Table[T[n - k - 1, k], {n, 1, 10}, {k, n - 1, 1, -1}] // Flatten (* Jean-François Alcover, Aug 29 2019 *) CROSSREFS Cf. A082157, A082161. Sequence in context: A198347 A019670 A093436 * A209634 A289523 A078220 Adjacent sequences:  A082166 A082167 A082168 * A082170 A082171 A082172 KEYWORD easy,nonn,tabl AUTHOR Valery A. Liskovets, Apr 09 2003 STATUS approved

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Last modified October 18 10:59 EDT 2019. Contains 328147 sequences. (Running on oeis4.)