A266589 Binary representation of the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 1110, 1000001, 111000, 11100000111, 11100000, 111110000011111, 1110000000, 1111111000001111111, 111000000000, 11111111100000111111111, 11100000000000, 111111111110000011111111111, 1110000000000000, 1111111111111000001111111111111, 111000000000000000

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, Jan 01 2016 and Apr 18 2019: (Start)

a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>7.

G.f.: (1 +10*x -8991*x^2 +898991*x^3 -10091010*x^4 +1009091010*x^5 +10100000*x^6 -1010100000*x^7) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 -100*x)*(1 +100*x)).

(End)

Conjecture: a(n) = (10*100^n - 99999*10^(n-2) - 1)/9 for odd n > 1; a(n) = 111*10^(n-1) for even n > 1. - Karl V. Keller, Jr., Oct 06 2021

Mathematica

rule=37; 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. A266588, A266590.

Sequence in context: A049064 A267246 A355316 * A015026 A130598 A267595

Adjacent sequences: A266586 A266587 A266588 * A266590 A266591 A266592

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved