A000282 Finite automata.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

References

• 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).

Links

• 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.

Crossrefs

Cf. A002854, A054732, A054747.

Programs

PARI

/* 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

Formula

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

Extensions

More terms from Vladeta Jovovic, Apr 22 2000

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