A266515 Binary representation of the n-th iteration of the "Rule 29" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 100, 1101111, 10000, 11110111111, 1000000, 111111011111111, 100000000, 1111111101111111111, 10000000000, 11111111110111111111111, 1000000000000, 111111111111011111111111111, 100000000000000, 1111111111111101111111111111111, 10000000000000000

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

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

Cf. A266514, A266516.

Sequence in context: A286023 A286643 A290861 * A036929 A168586 A330290

Adjacent sequences: A266512 A266513 A266514 * A266516 A266517 A266518

Keyword

nonn,easy

Author

Robert Price, Dec 30 2015

Status

approved