A259661 Binary representation of the middle column of the "Rule 54" elementary cellular automaton starting with a single ON (black) cell.
1, 11, 110, 1100, 11001, 110011, 1100110, 11001100, 110011001, 1100110011, 11001100110, 110011001100, 1100110011001, 11001100110011, 110011001100110, 1100110011001100, 11001100110011001, 110011001100110011, 1100110011001100110, 11001100110011001100
Offset: 0
Examples
From _Michael De Vlieger_, Dec 09 2015: (Start)
First 8 rows at left, ignoring "0" outside of range of 1's, the center column values in parentheses, and at right the value of center column cells up to that row:
(1) -> 1
1 (1) 1 -> 11
1 0 (0) 0 1 -> 110
1 1 1 (0) 1 1 1 -> 1100
1 0 0 0 (1) 0 0 0 1 -> 11001
1 1 1 0 1 (1) 1 0 1 1 1 -> 110011
1 0 0 0 1 0 (0) 0 1 0 0 0 1 -> 1100110
1 1 1 0 1 1 1 (0) 1 1 1 0 1 1 1 -> 11001100
1 0 0 0 1 0 0 0 (1) 0 0 0 1 0 0 0 1 -> 110011001
(End)
Links
- Robert Price, Table of n, a(n) for n = 0..999
- Eric Weisstein's World of Mathematics, Rule 54
- Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
- Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
- Index entries for sequences related to cellular automata
- Index to Elementary Cellular Automata
Programs
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Mathematica
lim = 20; Take[Last@ Take[#, Ceiling[Length[#]/2]] & /@ CellularAutomaton[54, {{1}, 0}, lim], #] & /@ Range@ lim (* Michael De Vlieger, Dec 09 2015 *)
Formula
Conjectures from Colin Barker, Dec 08 2015 and Apr 17 2019: (Start)
a(n) = 11*a(n-1) - 11*a(n-2) + 11*a(n-3) - 10*a(n-4) for n>3.
G.f.: 1 / ((1-x)*(1-10*x)*(1+x^2)).
(End)