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A082171
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A subclass of quasi-acyclic automata with 2 inputs, n transient and k absorbing labeled states.
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4
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Array read by antidiagonals: (0,1),(0,2),(1,1),(0,3),... The first column is A082159.
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REFERENCES
| 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
| V. A. Liskovets, Exact enumeration of acyclic deterministic automata,Discrete Appl. Math., 154, No.3 (2006), 537-551.
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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.
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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
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CROSSREFS
| Cf. A082163, A082169.
Sequence in context: A075847 A193602 A049967 * A164795 A201741 A197259
Adjacent sequences: A082168 A082169 A082170 * A082172 A082173 A082174
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Valery Liskovets (liskov(AT)im.bas-net.by), Apr 09 2003
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