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A267678 Decimal representation of the n-th iteration of the "Rule 197" elementary cellular automaton starting with a single ON (black) cell. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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.

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

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)