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Search: id:A082170
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| A082170 |
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Deterministic completely defined quasi-acyclic automata with 3 inputs, n transient and k absorbing labeled states. |
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5
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| 1, 1, 1, 1, 8, 15, 1, 27, 368, 1024, 1, 64, 2727, 53672, 198581, 1, 125, 11904, 710532, 18417792, 85102056, 1, 216, 38375, 4975936, 386023509, 12448430408, 68999174203, 1, 343, 101520, 23945000, 3977848832, 381535651512
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Array read by antidiagonals: (0,1),(0,2),(1,1),(0,3),... The first column is A082158.
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REFERENCES
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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
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V. A. Liskovets, Exact enumeration of acyclic deterministic automata,Discrete Appl. Math., 154, No.3 (2006), 537-551.
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FORMULA
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T(n, k)=T_3(n, k) where T_3(0, k) := 1, T_3(n, k) := sum(binomial(n, i)*(-1)^(n-i-1)*(i+k)^(3*n-3*i)*T_3(i, k), i=0..n-1), n>0;
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EXAMPLE
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The array begins:
1 1 1 1 1 1 1 1 - k=0
1 8 27 64 125 216 343 512 - k=1
15 368 2727 11904 38375 101520 233583 484352 - k=2
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CROSSREFS
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Cf. A082162, A082169.
Sequence in context: A009453 A050582 A128451 this_sequence A136377 A103706 A134990
Adjacent sequences: A082167 A082168 A082169 this_sequence A082171 A082172 A082173
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Valery Liskovets (liskov(AT)im.bas-net.by), Apr 09 2003
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