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A266283
Binary representation of the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell.
3
1, 10, 101, 1101010, 10101, 11110101010, 1010101, 111111010101010, 101010101, 1111111101010101010, 10101010101, 11111111110101010101010, 1010101010101, 111111111111010101010101010, 101010101010101, 1111111111111101010101010101010, 10101010101010101
OFFSET
0,2
FORMULA
From Colin Barker, Dec 27 2015 and Apr 14 2019: (Start)
a(n) = 10101*a(n-2) - 1010100*a(n-4) + 1000000*a(n-6) for n>5.
G.f.: (1+10*x-10000*x^2+1000000*x^3-1100000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).
(End)
a(n) = (10*100^n - (1000*10^n-1)/11 - 1)/9 for odd n; a(n) = (100*10^n-1)/99 for even n. - Karl V. Keller, Jr., Aug 29 2021
MATHEMATICA
rule=13; 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 - (1000*10**n-1)//11 - 1)//9 if n%2 else (100*10**n-1)//99 for n in range(50)]) # Karl V. Keller, Jr., Aug 29 2021
CROSSREFS
Sequence in context: A036299 A061107 A015498 * A309540 A039393 A199168
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 26 2015
STATUS
approved