A000282 Finite automata. (Formerly M3169 N1285)

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

Offset

1,1

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

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

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.

Formula

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

Prog

(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

Crossrefs

Cf. A002854, A054732, A054747.

Sequence in context: A061173 A156598 A082942 * A322775 A338408 A277413

Adjacent sequences: A000279 A000280 A000281 * A000283 A000284 A000285

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Apr 22 2000

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

Status

approved