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A266787
Binary representation of the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
2
1, 11, 1100, 1010111, 1111000, 11010001111, 1111010000, 111010001111111, 1111010000000, 1111010001111111111, 1111010000000000, 11111010001111111111111, 1111010000000000000, 111111010001111111111111111, 1111010000000000000000, 1111111010001111111111111111111
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 03 2016 and Apr 18 2019: (Start)
a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>10.
G.f.: (1 +11*x -9901*x^2 +889100*x^3 -979100*x^4 +7891000*x^5 -109001000*x^6 +1090110000*x^7 +9990000*x^8 -1100000000*x^9 +100000000*x^10) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 -1000*x^2)).
(End)
MATHEMATICA
rule=61; 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: A319424 A348269 A153435 * A109227 A133342 A110574
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 03 2016
STATUS
approved