A054747 -id:A054747 - cp's OEIS frontend

A000282 Finite automata.

3, 70, 3783, 338475, 40565585, 6061961733, 1083852977811, 225615988054171, 53595807366038234, 14308700593468127485, 4241390625289880226714, 1382214286200071777573643, 491197439886557439295166226, 189044982636675290371386547592, 78334771617452038208125184627931, 34771576300926271400714044414858372

Offset: 1

N. J. A. Sloane

nonn

Given the name of A054747, another name for this sequence can be "Number of inequivalent n-state 2-input 2-output connected automata with respect to an input permutation." - Petros Hadjicostas, Mar 08 2021

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Christian G. Bower, PARI programs for transforms, 2007.
Michael A. Harrison, A census of finite automata, Canad. J. Math., 17, No. 1, (1965), 100-113. [First apply Theorem 6.2 (p. 107) with k = p = 2 to get A054747. Then apply Theorem 7.2 (p. 110) to get the number of classes of connected automata counted by A054747. - _Petros Hadjicostas_, Mar 08 2021]
N. J. A. Sloane, Maple programs for transforms, 2001-2020.

Cf. A002854, A054732, A054747.

/* This program is a modification of Christian G. Bower's PARI program for the inverse Euler transform from the link above. */
lista(nn) = {local(A=vector(nn+1)); for(n=1, nn+1, A[n]=if(n==1, 1, A054747(n-1))); local(B=vector(#A-1,n,1/n),C); A[1] = 1; C = log(Ser(A)); A=vecextract(A,"2.."); for(i=1, #A, A[i] = polcoeff(C,i)); A = dirdiv(A,B); } \\ Petros Hadjicostas, Mar 08 2021

Inverse Euler transform of A054747. - Petros Hadjicostas, Mar 08 2021

More terms from Vladeta Jovovic, Apr 22 2000

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

A054052 Number of nonisomorphic n-state automata with binary inputs and outputs.

Original entry on oeis.org

4, 136, 7860, 703760, 83731616, 12434579448, 2213014106124, 459106576445584, 108787771126443552, 28987989805582701000, 8579866813375037411844, 2792769757495835238342624, 991517773420290134796904064, 381299821992680629261308708504, 157894902912089771345216547890976, 70047508374342247037912201234627760

Offset: 1

Vladeta Jovovic, Apr 29 2000

nonn

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

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).]

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

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, 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

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.]

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

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A000282 Finite automata.

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