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A082169
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Deterministic completely defined quasi-acyclic automata with 2 inputs, n transient and k absorbing labeled states.
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5
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Array read by antidiagonals: (0,1),(0,2),(1,1),(0,3),... The first column is A082157.
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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)=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;
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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
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CROSSREFS
| Cf. A082161.
Sequence in context: A198347 A019670 A093436 * A078220 A139346 A133390
Adjacent sequences: A082166 A082167 A082168 * A082170 A082171 A082172
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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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