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A063467
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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.
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1
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1, 1, 1, 3, 1, 9, 1, 53, 184, 813, 1, 144802
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OFFSET
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1,4
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COMMENTS
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a(n)=1 for prime values of n as we must factor to get nontrivial examples.
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REFERENCES
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T. Boykett, "Combinatorial construction of one-dimensional cellular automata", Contributions to General Algebra 9, 1994.
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LINKS
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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
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CROSSREFS
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Cf. A261864.
Sequence in context: A303552 A130599 A157674 * A223140 A021762 A019736
Adjacent sequences: A063464 A063465 A063466 * A063468 A063469 A063470
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KEYWORD
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nice,nonn,hard,more
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AUTHOR
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Tim Boykett (tim(AT)timesup.org), Jul 27 2001
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EXTENSIONS
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a(12) from Tim Boykett's 2004 article, page 244.
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STATUS
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approved
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