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A082171 A subclass of quasi-acyclic automata with 2 inputs, n transient and k absorbing labeled states. 4
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, 1627740504, 75325337235, 2483829653544, 42934911510249 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

The first column is A082159.

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)=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.

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

MATHEMATICA

T[0, _] = 1; T[n_, k_] := T[n, k] = Sum[Binomial[n, i] (-1)^(n - i - 1)*((i + k + 1)^2 - 1)^(n - i)*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. A082159, A082163, A082169.

Sequence in context: A049967 A221780 A221723 * A164795 A201741 A280192

Adjacent sequences:  A082168 A082169 A082170 * A082172 A082173 A082174

KEYWORD

easy,nonn,tabl

AUTHOR

Valery A. Liskovets, Apr 09 2003

STATUS

approved

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Last modified February 28 10:22 EST 2020. Contains 332323 sequences. (Running on oeis4.)