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%I #20 Jul 09 2022 12:19:49
%S 3,7,78,1388,35186,1132613,43997426,1993473480
%N The number E_{n,2} of n-state topological epsilon-machines over a binary alphabet.
%C Topological epsilon-machines are a class of minimal, deterministic finite automata with a single recurrent component all of whose states are start and final states. These, in turn, can be represented as a class of labeled directed graphs that are strongly connected. They also represent the skeletons of finite-memory stochastic processes or sofic subshifts.
%C Row sums of A181621. - _Jonathan Vos Post_, Nov 03 2010
%H B. D. Johnson, J. P. Crutchfield, C. J. Ellison and C. S. McTague, <a href="http://arxiv.org/abs/1011.0036">Enumerating Finitary Processes</a> arXiv:1011.0036 [cs.FL], 2010-2012.
%H S. Wolfram, <a href="https://www.wolframscience.com/nks/p957/">A New Kind of Science, Wolfram Media Inc., (2002), p. 957</a>.
%F a(n) = Sum_{e=1..n+1} A181621(e,i) = Sum_{k=1..n+1} E(n;2) of binary-alphabet topological epsilon-machines with n states and k edges. - _Jonathan Vos Post_, Nov 03 2010
%Y Cf. A181621.
%K hard,nonn
%O 1,1
%A _James P. Crutchfield_, Oct 30 2010
%E a(8) from _James P. Crutchfield_, Nov 22 2010
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