%I #29 Mar 22 2020 09:26:42
%S 1,1,1,3,1,9,1,53,184,813,1,144802
%N Number of idempotent reversible binary (i.e., radius one half) cellular automata of order n. Equivalently, number of loop-noded symmetric 2-colored unique 2-path graphs on n nodes. Equivalently, number of idempotent semicentral bigroupoids of order n.
%C a(n)=1 for prime values of n as we must factor to get nontrivial examples.
%D T. Boykett, "Combinatorial construction of one-dimensional cellular automata", Contributions to General Algebra 9, 1994.
%H T. Boykett, <a href="http://www.algebra.uni-linz.ac.at/~tim/enumeration.ps.gz">Efficient exhaustive enumeration of one dimensional reversible cellular automata</a>, 2001.
%H Tim Boykett, <a href="http://dx.doi.org/10.1016/j.tcs.2004.06.007">Efficient exhaustive listings of reversible one dimensional cellular automata</a>, Theoretical Computer Science 325 (2004) 215-247.
%H D. Hillman, <a href="http://dx.doi.org/10.1016/0167-2789(91)90128-V">The structure of reversible one-dimensional cellular automata</a>, Physica D, 52:277-292, 1991.
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%Y Cf. A261864.
%K nice,nonn,hard,more
%O 1,4
%A Tim Boykett (tim(AT)timesup.org), Jul 27 2001
%E a(12) from Tim Boykett's 2004 article, page 244.