|
|
A267677
|
|
Binary representation of the n-th iteration of the "Rule 197" elementary cellular automaton starting with a single ON (black) cell.
|
|
2
|
|
|
1, 10, 10100, 1101000, 111010100, 11110101000, 1111101010100, 111111010101000, 11111110101010100, 1111111101010101000, 111111111010101010100, 11111111110101010101000, 1111111111101010101010100, 111111111111010101010101000, 11111111111110101010101010100
(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 19 2016 and Apr 20 2019: (Start)
a(n) = 110*a(n-1)-999*a(n-2)-110*a(n-3)+1000*a(n-4) for n>5.
G.f.: (1-100*x+9999*x^2+100*x^3-9900*x^4-10000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1-100*x)).
(End)
|
|
MATHEMATICA
|
rule=197; 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
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|