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A267924 Decimal representation of the n-th iteration of the "Rule 245" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 27, 123, 507, 2043, 8187, 32763, 131067, 524283, 2097147, 8388603, 33554427, 134217723, 536870907, 2147483643, 8589934587, 34359738363, 137438953467, 549755813883, 2199023255547, 8796093022203, 35184372088827, 140737488355323, 562949953421307 (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 23 2016 and Apr 20 2019: (Start)

a(n) = 5*a(n-1)-4*a(n-2) for n>2.

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

(End)

Empirical a(n) = 2^(2*n+1) - 5 for n>0. - Colin Barker, Nov 26 2016 and Apr 20 2019

MATHEMATICA

rule=245; 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. A267922.

Sequence in context: A127210 A161807 A261716 * A241678 A063263 A204809

Adjacent sequences:  A267921 A267922 A267923 * A267925 A267926 A267927

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 22 2016

STATUS

approved

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Last modified August 18 00:56 EDT 2019. Contains 326059 sequences. (Running on oeis4.)