login
A267350
Binary representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell.
2
1, 101, 1110, 1110111, 111000, 11111011111, 11100000, 111111101111111, 1110000000, 1111111110111111111, 111000000000, 11111111111011111111111, 11100000000000, 111111111111101111111111111, 1110000000000000, 1111111111111110111111111111111, 111000000000000000
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 14 2016: (Start)
a(n) = 10101*a(n-2) - 1010100*a(n-4) + 1000000*a(n-6) for n > 6.
G.f.: (1 + 101*x - 8991*x^2 + 89910*x^3 - 10091010*x^4 - 200000*x^5 + 10100000*x^6) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).
(End)
MATHEMATICA
rule=123; 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
Sequence in context: A280340 A283589 A284403 * A290526 A290827 A290835
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 13 2016
EXTENSIONS
Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022
STATUS
approved