A071033 a(n) = n-th state of cellular automaton generated by "Rule 94" when started with a single ON cell.
1, 111, 11011, 1110111, 110101011, 11101010111, 1101010101011, 111010101010111, 11010101010101011, 1110101010101010111, 110101010101010101011, 11101010101010101010111, 1101010101010101010101011, 111010101010101010101010111, 11010101010101010101010101011
Offset: 0
Links
- 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).
Programs
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Mathematica
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 *)
Formula
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
Extensions
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
Comments