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A267938 Decimal representation of the n-th iteration of the "Rule 251" elementary cellular automaton starting with a single ON (black) cell. 2
1, 5, 31, 127, 511, 2047, 8191, 32767, 131071, 524287, 2097151, 8388607, 33554431, 134217727, 536870911, 2147483647, 8589934591, 34359738367, 137438953471, 549755813887, 2199023255551, 8796093022207, 35184372088831, 140737488355327, 562949953421311 (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 16 2019: (Start)

a(n) = 5*a(n-1)-4*a(n-2) for n>3.

G.f.: (1+10*x^2-8*x^3) / ((1-x)*(1-4*x)).

(End)

Empirical a(n) = 2^(2*n+1) - 1 for n>1. - Colin Barker, Nov 25 2016

MATHEMATICA

rule=251; 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. A267936.

Sequence in context: A053699 A152122 A260045 * A041303 A184446 A077719

Adjacent sequences:  A267935 A267936 A267937 * A267939 A267940 A267941

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 22 2016

STATUS

approved

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Last modified December 5 16:21 EST 2019. Contains 329753 sequences. (Running on oeis4.)