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A266515
Binary representation of the n-th iteration of the "Rule 29" elementary cellular automaton starting with a single ON (black) cell.
2
1, 11, 100, 1101111, 10000, 11110111111, 1000000, 111111011111111, 100000000, 1111111101111111111, 10000000000, 11111111110111111111111, 1000000000000, 111111111111011111111111111, 100000000000000, 1111111111111101111111111111111, 10000000000000000
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Dec 31 2015 and Apr 16 2019: (Start)
a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>5.
G.f.: (1+11*x-10001*x^2+990000*x^3+10000*x^4-1100000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).
(End)
Conjecture: a(n) = (10*(100^n - 9*10^n) - 1)/9 for odd n; a(n) = 10^n for even n. - Karl V. Keller, Jr., Oct 03 2021
MATHEMATICA
rule=29; 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: A286023 A286643 A290861 * A036929 A168586 A330290
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 30 2015
STATUS
approved