|
|
A267002
|
|
Binary representation of the n-th iteration of the "Rule 83" elementary cellular automaton starting with a single ON (black) cell.
|
|
2
|
|
|
1, 101, 1000, 1101111, 1000000, 11101111111, 1000000000, 111101111111111, 1000000000000, 1111101111111111111, 1000000000000000, 11111101111111111111111, 1000000000000000000, 111111101111111111111111111, 1000000000000000000000, 1111111101111111111111111111111
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
Conjectures from Colin Barker, Jan 08 2016 and Apr 19 2019: (Start)
a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>5.
G.f.: (1+101*x-10001*x^2-9990*x^3+10000*x^4-1100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).
(End)
|
|
MATHEMATICA
|
rule=83; 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
|
|
|
|