|
|
A267051
|
|
Binary representation of the n-th iteration of the "Rule 92" elementary cellular automaton starting with a single ON (black) cell.
|
|
3
|
|
|
1, 11, 111, 1011, 10111, 101011, 1010111, 10101011, 101010111, 1010101011, 10101010111, 101010101011, 1010101010111, 10101010101011, 101010101010111, 1010101010101011, 10101010101010111, 101010101010101011, 1010101010101010111, 10101010101010101011
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
REFERENCES
|
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
|
|
LINKS
|
|
|
FORMULA
|
Conjectures from Colin Barker, Jan 10 2016 and Apr 17 2019: (Start)
a(n) = (539+450*(-1)^n+10^(2+n))/99 for n>0.
a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>3.
G.f.: (1+x-100*x^3) / ((1-x)*(1+x)*(1-10*x)).
(End)
|
|
MATHEMATICA
|
rule=92; 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 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|