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Search: id:A082172
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| A082172 |
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A subclass of quasi-acyclic automata with 3 inputs, n transient and k absorbing labeled states. |
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4
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| 1, 1, 7, 1, 26, 315, 1, 63, 2600, 45682, 1, 124, 11655, 675194, 15646589, 1, 215, 37944, 4861458, 366349152, 10567689552, 1, 342, 100835, 23641468, 3882676581, 361884843866, 12503979423607, 1, 511, 232560, 89076650, 26387681120
(list; table; graph; listen)
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OFFSET
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0,3
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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 A082160.
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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)=S_3(n, k) where S_3(0, k) := 1, S_3(n, k) := sum(binomial(n, i)*(-1)^(n-i-1)*((i+k+1)^3-1)^(n-i)*S_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
7 26 63 124 215 342 511 728 - k=1
315 2600 11655 37944 100835 232560 482895 924560 - k=2
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CROSSREFS
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Cf. A082164, A082170, A082171.
Adjacent sequences: A082169 A082170 A082171 this_sequence A082173 A082174 A082175
Sequence in context: A050310 A019431 A064051 this_sequence A053288 A050301 A083994
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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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