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%I #25 Mar 08 2021 22:51:18
%S 3,76,4003,352744,41876694,6217447912,1106509486839,229553329028386,
%T 54393886281136386,14493994916221695566,4289933406949379595583,
%U 1396384878753272032544946,495758886710258565409900342,190649910996342815795394676340,78947451456044942567072721038672,35023754187171124856459358053765838
%N Number of inequivalent n-state 2-input 2-output automata with respect to an input permutation.
%D F. Harary and E. Palmer, Graphical Enumeration, 1973.
%H Michael A. Harrison, <a href="http://dx.doi.org/10.4153/CJM-1965-010-9">A census of finite automata</a>, Canad. J. Math., 17, No. 1, (1965), 100-113. [See Theorem 6.2 with k = p = 2 (p. 107) and Table IV (p. 112).]
%o (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,
%o inc()=!forstep(i=n, 1, -1, p[i]<n\i && p[i]++ && return; p[i]=0), t); until(inc(), t=0; for( i=1, n, if( n < t+=i*p[i], until(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
%Y Cf. A002854, A054732.
%Y Euler transform of A000282.
%K nonn
%O 1,1
%A _Vladeta Jovovic_, Apr 22 2000
%E Terms a(14)-a(16) from _Petros Hadjicostas_, Mar 08 2021
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