%I #25 Dec 19 2021 12:07:04
%S 4,136,7860,703760,83731616,12434579448,2213014106124,459106576445584,
%T 108787771126443552,28987989805582701000,8579866813375037411844,
%U 2792769757495835238342624,991517773420290134796904064,381299821992680629261308708504,157894902912089771345216547890976,70047508374342247037912201234627760
%N Number of nonisomorphic n-state automata with binary inputs and outputs.
%D F. Harary and E. Palmer, Graphical Enumeration, 1973.
%H M. 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 p. 107 (Theorem 6.1 with k = p = 2) and p. 112 (Table III).]
%F a(n) = Sum_{1*s_1+2*s_2+...=n} fixA[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...), where fixA[s_1, s_2, ...] = Product_{i>=1} (Sum_{d|i} 2*d*s_d)^(2*s_i). - [Modified from _Christian G. Bower_'s contribution in A054050 by _Petros Hadjicostas_, Mar 08 2021 using Theorem 6.1 in Harrison (1965) with k = 2 inputs and p = 2 outputs.]
%o (PARI) A054052(n) = {local(p=vector(n)); my(S=0, A() = prod(i=1, n, sumdiv(i, d, 2*d*p[d])^(2*p[i])), 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, A054050, A054747, A054732, A054053.
%K nonn
%O 1,1
%A _Vladeta Jovovic_, Apr 29 2000
%E Terms a(14)-a(16) from _Petros Hadjicostas_, Mar 08 2021.