A267780 Decimal representation of the n-th iteration of the "Rule 211" elementary cellular automaton starting with a single ON (black) cell.

1, 5, 25, 125, 505, 2045, 8185, 32765, 131065, 524285, 2097145, 8388605, 33554425, 134217725, 536870905, 2147483645, 8589934585, 34359738365, 137438953465, 549755813885, 2199023255545, 8796093022205, 35184372088825, 140737488355325, 562949953421305

Offset

0,2

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 20 2016 and Apr 20 2019: (Start)

a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3) for n>3.

G.f.: (1+x+4*x^2+24*x^3) / ((1-x)*(1+x)*(1-4*x)).

(End)

Mathematica

rule=211; 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]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

Crossrefs

Cf. A267778, A267779.

Sequence in context: A015950 A337950 A366323 * A228736 A126642 A269615

Adjacent sequences: A267777 A267778 A267779 * A267781 A267782 A267783

Keyword

nonn,easy

Author

Robert Price, Jan 20 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022

Status

approved