A267937 Binary representation of the n-th iteration of the "Rule 251" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 11111, 1111111, 111111111, 11111111111, 1111111111111, 111111111111111, 11111111111111111, 1111111111111111111, 111111111111111111111, 11111111111111111111111, 1111111111111111111111111, 111111111111111111111111111, 11111111111111111111111111111

Offset

0,2

Comments

Seems to differ from A267889, A267887 and A100706 only at a(1). - R. J. Mathar, Jun 24 2025

References

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

Links

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

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Jan 23 2016 and Apr 16 2019: (Start)

a(n) = 101*a(n-1)-100*a(n-2) for n>3.

G.f.: (1+1010*x^2-1000*x^3) / ((1-x)*(1-100*x)).

(End)

Mathematica

rule=251; 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. A267936.

Sequence in context: A267920 A300570 A171825 * A185893 A385144 A156669

Adjacent sequences: A267934 A267935 A267936 * A267938 A267939 A267940

Keyword

nonn,easy

Author

Robert Price, Jan 22 2016

Status

approved