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A266838
Binary representation of the n-th iteration of the "Rule 67" elementary cellular automaton starting with a single ON (black) cell.
3
1, 100, 1010, 1100001, 1011100, 11100001011, 1011100000, 111100001011111, 1011100000000, 1111100001011111111, 1011100000000000, 11111100001011111111111, 1011100000000000000, 111111100001011111111111111, 1011100000000000000000, 1111111100001011111111111111111
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 05 2016 and Apr 18 2019: (Start)
a(n) = 11001*a(n-2) - 10011000*a(n-4) + 10000000*a(n-6) for n > 9.
G.f.: (1 + 100*x - 9991*x^2 - 99*x^3 - 88910*x^4 - 9990*x^5 - 10901100*x^6 - 99900*x^7 + 11000000*x^8 - 1000000*x^9) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).
(End)
Conjecture: a(n) = (10*100^n - 999909*1000^floor(n/2)/10000 - 1)/9 for odd n > 3; a(n) = 10111*1000^(n/2)/10000 for even n > 3. - Karl V. Keller, Jr., Dec 16 2021
MATHEMATICA
rule=67; 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: A173484 A136387 A001737 * A267127 A266893 A267153
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 04 2016
STATUS
approved