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A266984 Decimal representation of the n-th iteration of the "Rule 81" elementary cellular automaton starting with a single ON (black) cell. 2
1, 1, 24, 31, 384, 511, 6144, 8191, 98304, 131071, 1572864, 2097151, 25165824, 33554431, 402653184, 536870911, 6442450944, 8589934591, 103079215104, 137438953471, 1649267441664, 2199023255551, 26388279066624, 35184372088831, 422212465065984, 562949953421311 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 08 2016 and Apr 17 2019: (Start)

a(n) = ((-4)^n+(-1)^n-1)/2+4^n for n>0.

a(n) = 17*a(n-2)-16*a(n-4) for n>4.

G.f.: (1+2*x)*(1-x+9*x^2-4*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

(End)

MATHEMATICA

rule=81; 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. A266982.

Sequence in context: A167307 A161378 A206448 * A217158 A214227 A337055

Adjacent sequences:  A266981 A266982 A266983 * A266985 A266986 A266987

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 07 2016

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)