A054053 Number of nonisomorphic connected n-state automata with binary inputs and outputs.

4, 126, 7336, 665120, 80038860, 11992785628, 2148752458832, 448000621008112, 106551292402319492, 28471977293653977714, 8445425847422222518488, 2753705028193531309816184, 978990839708922602845440908, 376905974468378563863272876248, 156221832236610857130449469228920, 69360325968752963320307268181976608

Offset: 1

Author

Vladeta Jovovic, Apr 29 2000

Keywords

• nonn

Comments

Inverse Euler transform of A054052.

References

• F. Harary and E. Palmer, Graphical Enumeration, 1973. [See Section 6.5, pp. 146-150.]

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. [See Table III, p. 112.]
• N. J. A. Sloane, Maple program for transforms, 2001-2020.

Crossrefs

Cf. A000282, A054052, A054742.

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, A054052(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

Extensions

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