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A071033
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a(n) = n-th state of cellular automaton generated by "Rule 94" when started with a single ON cell.
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3
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1, 111, 11011, 1110111, 110101011, 11101010111, 1101010101011, 111010101010111, 11010101010101011, 1110101010101010111, 110101010101010101011, 11101010101010101010111, 1101010101010101010101011, 111010101010101010101010111, 11010101010101010101010101011
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OFFSET
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0,2
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COMMENTS
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a(n) has length 2n+1.
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LINKS
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Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Rule 94
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
Index to Elementary Cellular Automata
Index entries for sequences related to cellular automata
Index entries for linear recurrences with constant coefficients, signature (0,10001,0,-10000).
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FORMULA
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Conjecture: a(n) = floor((1099*100^n + 9090)/990) + 1 for odd n > 1; a(n) = floor((1090*100^n + 10)/990) + 1 for even n > 1. - Karl V. Keller, Jr., Oct 25 2021
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MATHEMATICA
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rule=94; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]]], {k, 1, rows}] (* Binary Representation of Rows *) (* Robert Price, Feb 21 2016 *)
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CROSSREFS
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This sequence, A118101 and A118102 are equivalent descriptions of the Rule 94 automaton.
Sequence in context: A266809 A152764 A249183 * A267364 A265379 A265688
Adjacent sequences: A071030 A071031 A071032 * A071034 A071035 A071036
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KEYWORD
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nonn,easy
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AUTHOR
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Hans Havermann, May 26 2002
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EXTENSIONS
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Corrected by Hans Havermann, Jan 07 2012
Edited by N. J. A. Sloane, Oct 20 2015 at the suggestion of Michael De Vlieger and Kevin Ryde
More terms from Robert Price, Dec 06 2015
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STATUS
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approved
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