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A082169 Deterministic completely defined quasi-acyclic automata with 2 inputs, n transient and k absorbing labeled states. 5
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, 13598786979, 254821480596, 1681740027657 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Array read by antidiagonals: (0,1),(0,2),(1,1),(0,3),...

The first column is A082157.

LINKS

Table of n, a(n) for n=0..44.

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)=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;

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

MATHEMATICA

T[0, _] = 1; T[n_, k_] := T[n, k] = Sum[Binomial[n, i] (-1)^(n - i - 1)*(i + k)^(2n - 2i) T[i, k], {i, 0, n - 1}];

Table[T[n - k - 1, k], {n, 1, 10}, {k, n - 1, 1, -1}] // Flatten (* Jean-Fran├žois Alcover, Aug 29 2019 *)

CROSSREFS

Cf. A082157, A082161.

Sequence in context: A198347 A019670 A093436 * A209634 A289523 A078220

Adjacent sequences:  A082166 A082167 A082168 * A082170 A082171 A082172

KEYWORD

easy,nonn,tabl

AUTHOR

Valery A. Liskovets, Apr 09 2003

STATUS

approved

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Last modified October 18 10:59 EDT 2019. Contains 328147 sequences. (Running on oeis4.)