A267678 Decimal representation of the n-th iteration of the "Rule 197" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 20, 104, 468, 1960, 8020, 32424, 130388, 522920, 2094420, 8383144, 33543508, 134195880, 536827220, 2147396264, 8589759828, 34359388840, 137438254420, 549754415784, 2199020459348, 8796087429800, 35184360904020, 140737465985704, 562949908682068

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 19 2016: (Start)

a(n) = 6*a(n-1)-7*a(n-2)-6*a(n-3)+8*a(n-4) for n>5.

G.f.: (1-4*x+15*x^2+4*x^3-12*x^4-16*x^5) / ((1-x)*(1+x)*(1-2*x)*(1-4*x)).

(End)

Conjecture: a(n) = 2*(-3 + (-1)^n - 2^(2+n) + 3*4^n)/3 for n>1. - Colin Barker, Feb 14 2017

Conjecture: a(n) = floor((6*4^n - 8*2^n)/3) - 2^(n mod 2) for n > 1. - Karl V. Keller, Jr., Jun 01 2022

Mathematica

rule=197; 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. A267676, A267677.

Sequence in context: A035599 A222556 A103101 * A009357 A052361 A001884

Adjacent sequences: A267675 A267676 A267677 * A267679 A267680 A267681

Keyword

nonn

Author

Robert Price, Jan 19 2016

Status

approved