A267774 Decimal representation of the n-th iteration of the "Rule 207" elementary cellular automaton starting with a single ON (black) cell.

1, 6, 29, 123, 503, 2031, 8159, 32703, 130943, 524031, 2096639, 8387583, 33552383, 134213631, 536862719, 2147467263, 8589901823, 34359672831, 137438822399, 549755551743, 2199022731263, 8796091973631, 35184369991679, 140737484161023, 562949945032703

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) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>3.

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

(End)

Mathematica

rule=207; 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. A267773, A267775.

Sequence in context: A326805 A061648 A281050 * A243474 A111644 A225618

Adjacent sequences: A267771 A267772 A267773 * A267775 A267776 A267777

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. - Michael De Vlieger, Jun 13 2022

Status

approved