A054747 Number of inequivalent n-state 2-input 2-output automata with respect to an input permutation.

3, 76, 4003, 352744, 41876694, 6217447912, 1106509486839, 229553329028386, 54393886281136386, 14493994916221695566, 4289933406949379595583, 1396384878753272032544946, 495758886710258565409900342, 190649910996342815795394676340, 78947451456044942567072721038672, 35023754187171124856459358053765838

Offset: 1

Author

Vladeta Jovovic, Apr 22 2000

Keywords

• nonn

References

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

Links

• Michael A. Harrison, A census of finite automata, Canad. J. Math., 17, No. 1, (1965), 100-113. [See Theorem 6.2 with k = p = 2 (p. 107) and Table IV (p. 112).]

Crossrefs

Cf. A002854, A054732.

Euler transform of A000282.

Programs

PARI

A054747(n)={local(p=vector(n)); local(q=matrix(2,2)); q[1,1] = 2; q[1,2] = 0; q[2,1]=0; q[2,2]=1; my(S=0, A() = sum(j=1, 2, prod(r=1, n, prod(s=1, 2, (2*sumdiv(lcm(r,s), d, if(d < n+1, d*p[d], 0)))^(p[r]*q[j,s]*gcd(r,s)))))/2,
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

Extensions

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