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A266609
Binary representation of the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
2
1, 0, 101, 1100100, 1, 11111111000, 101, 111111111100100, 1, 1111111111111111000, 101, 11111111111111111100100, 1, 111111111111111111111111000, 101, 1111111111111111111111111100100, 1, 11111111111111111111111111111111000, 101
OFFSET
0,3
FORMULA
Conjectures from Colin Barker, Jan 02 2016 and Apr 18 2019: (Start)
a(n) = 10000*a(n-2)+a(n-4)-10000*a(n-6) for n>5.
G.f.: (1-9899*x^2+1100100*x^3-1010000*x^4+110111000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1+x^2)).
(End)
Conjecture: a(n) = floor((10*100^n + 10 - 1010*(n mod 4))/9) - 10675*0^((n+1) mod 4) for odd n; a(n) = 101^((n mod 4)/2) for even n. - Karl V. Keller, Jr., Oct 07 2021
MATHEMATICA
rule=41; 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: A317957 A266244 A138120 * A082521 A365994 A262645
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 01 2016
STATUS
approved