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A267877 Decimal representation of the n-th iteration of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell. 1
1, 0, 21, 119, 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

0,3

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

Index entries for linear recurrences with constant coefficients, signature (5,-4).

FORMULA

From Colin Barker, Jan 22 2016: (Start)

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

G.f.: (1-5*x+25*x^2+14*x^3-32*x^5) / ((1-x)*(1-4*x)).

(End)

a(n) = 2^(2*n+1) - 1 for n>3. - Colin Barker, Nov 26 2016

MATHEMATICA

rule=233; 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 *)

PROG

(PARI) Vec((1-5*x+25*x^2+14*x^3-32*x^5)/((1-x)*(1-4*x)) + O(x^30)) \\ Colin Barker, Jan 22 2016

CROSSREFS

Cf. A267868.

Sequence in context: A054257 A297316 A079417 * A183318 A204214 A074088

Adjacent sequences:  A267874 A267875 A267876 * A267878 A267879 A267880

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 21 2016

STATUS

approved

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Last modified January 21 11:44 EST 2019. Contains 319354 sequences. (Running on oeis4.)