A063467 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.

1, 1, 1, 3, 1, 9, 1, 53, 184, 813, 1, 144802

Offset

1,4

Comments

a(n)=1 for prime values of n as we must factor to get nontrivial examples.

References

T. Boykett, "Combinatorial construction of one-dimensional cellular automata", Contributions to General Algebra 9, 1994.

Links

Table of n, a(n) for n=1..12.

T. Boykett, Efficient exhaustive enumeration of one dimensional reversible cellular automata, 2001.

Tim Boykett, Efficient exhaustive listings of reversible one dimensional cellular automata, Theoretical Computer Science 325 (2004) 215-247.

D. Hillman, The structure of reversible one-dimensional cellular automata, Physica D, 52:277-292, 1991.

Index entries for sequences related to cellular automata

Crossrefs

Cf. A261864.

Sequence in context: A130599 A157674 A360752 * A223140 A021762 A019736

Adjacent sequences: A063464 A063465 A063466 * A063468 A063469 A063470

Keyword

nice,nonn,hard,more

Author

Tim Boykett (tim(AT)timesup.org), Jul 27 2001

Extensions

a(12) from Tim Boykett's 2004 article, page 244.

Status

approved