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 A082171 A subclass of quasi-acyclic automata with 2 inputs, n transient and k absorbing labeled states. 4
 1, 1, 3, 1, 8, 39, 1, 15, 176, 1206, 1, 24, 495, 7784, 69189, 1, 35, 1104, 29430, 585408, 6416568, 1, 48, 2135, 84600, 2791125, 67481928, 881032059, 1, 63, 3744, 204470, 9841728, 389244600, 11111547520, 168514815360, 1, 80, 6111, 437616, 28569765, 1627740504, 75325337235, 2483829653544, 42934911510249 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Array read by antidiagonals: (0,1),(0,2),(1,1),(0,3),... The first column is A082159. 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)=S_2(n, k) where S_2(0, k) := 1, S_2(n, k) := sum(binomial(n, i)*(-1)^(n-i-1)*((i+k+1)^2-1)^(n-i)*S_2(i, k), i=0..n-1), n>0. EXAMPLE The array begins: 1 1 1 1 1 1 1 1 1 - k=0 3 8 15 24 35 48 63 80 99 - k=1 39 176 495 1104 2135 3744 6111 9440 13959 - k=2 MATHEMATICA T[0, _] = 1; T[n_, k_] := T[n, k] = Sum[Binomial[n, i] (-1)^(n - i - 1)*((i + k + 1)^2 - 1)^(n - i)*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. A082159, A082163, A082169. Sequence in context: A049967 A221780 A221723 * A164795 A201741 A280192 Adjacent sequences:  A082168 A082169 A082170 * A082172 A082173 A082174 KEYWORD easy,nonn,tabl AUTHOR Valery A. Liskovets, Apr 09 2003 STATUS approved

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Last modified February 28 10:22 EST 2020. Contains 332323 sequences. (Running on oeis4.)