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A082160 Deterministic completely defined acyclic automata with 3 inputs and n+1 transient labeled states including a unique state having all transitions to the absorbing state. 3
1, 7, 315, 45682, 15646589, 10567689552, 12503979423607, 23841011541867520, 68835375121428936153, 286850872894190847235840, 1660638682341609286358474579, 12947089879912710544534553836032 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is the first column of the array A082172.

LINKS

Table of n, a(n) for n=0..11.

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

a(n)=b_3(n) where b_3(0) := 1, b_3(n) := sum(binomial(n, i)*(-1)^(n-i-1)*((i+2)^3-1)^(n-i)*b_3(i), i=0..n-1), n>0.

MATHEMATICA

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, i] (-1)^(n - i - 1) ((i + 2)^3 - 1)^(n - i) a[i], {i, 0, n - 1}];

Table[a[n], {n, 0, 11}] (* Jean-Fran├žois Alcover, Aug 29 2019 *)

CROSSREFS

Cf. A082159, A082158, A082172.

Sequence in context: A171148 A219267 A244851 * A220278 A163437 A109059

Adjacent sequences:  A082157 A082158 A082159 * A082161 A082162 A082163

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Apr 09 2003

STATUS

approved

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)