A265427 Binary representation of the n-th iteration of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 101, 1111, 11101, 110111, 1011101, 11110111, 111011101, 1101110111, 10111011101, 111101110111, 1110111011101, 11011101110111, 101110111011101, 1111011101110111, 11101110111011101, 110111011101110111, 1011101110111011101, 11110111011101110111

Offset: 0

Author

Robert Price, Dec 08 2015

Keywords

• nonn
• easy

Examples

			From _Michael De Vlieger_, Dec 09 2015: (Start)
First 12 rows:
1
1 1
1 0 1
1 1 1 1
1 1 1 0 1
1 1 0 1 1 1
1 0 1 1 1 0 1
1 1 1 1 0 1 1 1
1 1 1 0 1 1 1 0 1
1 1 0 1 1 1 0 1 1 1
1 0 1 1 1 0 1 1 1 0 1
1 1 1 1 0 1 1 1 0 1 1 1
1 1 1 0 1 1 1 0 1 1 1 0 1
(End)
		

References

• S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

• Robert Price, Table of n, a(n) for n = 0..999
• Eric Weisstein's World of Mathematics, Rule 188
• Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
• Index entries for sequences related to cellular automata
• Index to Elementary Cellular Automata

Crossrefs

Cf. A118173, A118174.

Programs

Mathematica

rule = 188; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule,{{1},0}, rows-1, {All,All}][[k]], {rows-k+1, rows+k-1}], {k,1,rows}][[k]]], {k,1,rows}]

Formula

Conjectures from Colin Barker, Dec 09 2015 and Apr 18 2019: (Start)

a(n) = a(n-2) + 10000*a(n-4) - 10000*a(n-6) for n>5.

G.f.: (1+11*x+100*x^2+1100*x^3+1000*x^4-1000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1+100*x^2)).

(End)

Conjecture: a(n) = floor(11100*100^n/9999) + 10^n - floor(11100*10^n/9999)*10^n. - Karl V. Keller, Jr., Dec 15 2021