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A266323
Binary representation of the n-th iteration of the "Rule 19" elementary cellular automaton starting with a single ON (black) cell.
3
1, 101, 0, 1111111, 0, 11111111111, 0, 111111111111111, 0, 1111111111111111111, 0, 11111111111111111111111, 0, 111111111111111111111111111, 0, 1111111111111111111111111111111, 0, 11111111111111111111111111111111111, 0, 111111111111111111111111111111111111111
OFFSET
0,2
FORMULA
From Colin Barker, Dec 28 2015 and Apr 15 2019: (Start)
a(n) = 10001*a(n-2) - 10000*a(n-4) for n>5.
G.f.: (1+101*x-10001*x^2+101010*x^3+10000*x^4-100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
a(n) = (10*100^n - 1)/9*(n mod 2) + 0^n - 10*0^abs(n-1). - Karl V. Keller, Jr., Sep 02 2021
MATHEMATICA
rule=19; 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 *)
PROG
(Python) print([(10*100**n - 1)//9*(n%2) + 0**n - 10*0**abs(n-1) for n in range(50)]) # Karl V. Keller, Jr., Sep 02 2021
CROSSREFS
Sequence in context: A279699 A279602 A168588 * A280372 A181721 A277917
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 27 2015
STATUS
approved