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A267002 Binary representation of the n-th iteration of the "Rule 83" elementary cellular automaton starting with a single ON (black) cell. 1
1, 101, 1000, 1101111, 1000000, 11101111111, 1000000000, 111101111111111, 1000000000000, 1111101111111111111, 1000000000000000, 11111101111111111111111, 1000000000000000000, 111111101111111111111111111, 1000000000000000000000, 1111111101111111111111111111111 (list; graph; refs; listen; history; text; internal format)



S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.


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


Conjectures from Colin Barker, Jan 08 2016 and Apr 19 2019: (Start)

a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>5.

G.f.: (1+101*x-10001*x^2-9990*x^3+10000*x^4-1100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).



rule=83; 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]]], {k, 1, rows}] (* Binary Representation of Rows *)


Cf. A267001.

Sequence in context: A167842 A244369 A200733 * A242138 A171764 A164842

Adjacent sequences:  A266999 A267000 A267001 * A267003 A267004 A267005




Robert Price, Jan 08 2016



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Last modified December 13 09:58 EST 2019. Contains 329968 sequences. (Running on oeis4.)