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A054052 Number of nonisomorphic n-state automata with binary inputs and outputs. 3
4, 136, 7860, 703760, 83731616, 12434579448, 2213014106124, 459106576445584, 108787771126443552, 28987989805582701000, 8579866813375037411844, 2792769757495835238342624, 991517773420290134796904064, 381299821992680629261308708504, 157894902912089771345216547890976, 70047508374342247037912201234627760 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

F. Harary and E. Palmer, Graphical Enumeration, 1973.

LINKS

Table of n, a(n) for n=1..16.

M. A. Harrison, A census of finite automata, Canad. J. Math., 17, No. 1, (1965), 100-113. [See p. 107 (Theorem 6.1 with k = p = 2) and p. 112 (Table III).]

FORMULA

a(n) = Sum_{1*s_1+2*s_2+...=n} fixA[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...), where fixA[s_1, s_2, ...] = Product_{i>=1} (Sum_{d|i} 2*d*s_d)^(2*s_i). - [Modified from Christian G. Bower's contribution in A054050 by Petros Hadjicostas, Mar 08 2021 using Theorem 6.1 in Harrison (1965) with k = 2 inputs and p = 2 outputs.]

PROG

(PARI) A054052(n) = {local(p=vector(n)); my(S=0, A() = prod(i=1, n, sumdiv(i, d, 2*d*p[d])^(2*p[i])), inc()=!forstep(i=n, 1, -1, p[i]<n\i && p[i]++ && return; p[i]=0), t); until(inc(), t=0; for( i=1, n, if( n < t+=i*p[i], until(i++>n, p[i]=n); next(2))); t==n && S+ = A()/prod(i=1, n, i^p[i]*p[i]!)); S} \\ This is a modification of M. F. Hasler's PARI program from A002854. - Petros Hadjicostas, Mar 08 2021

CROSSREFS

Cf. A002854, A054050, A054747, A054732, A054053.

Sequence in context: A202299 A024264 A012052 * A012070 A001374 A229416

Adjacent sequences:  A054049 A054050 A054051 * A054053 A054054 A054055

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Apr 29 2000

EXTENSIONS

Terms a(14)-a(16) from Petros Hadjicostas, Mar 08 2021.

STATUS

approved

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Last modified October 3 17:25 EDT 2022. Contains 357237 sequences. (Running on oeis4.)