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A267003 Decimal representation of the n-th iteration of the "Rule 83" elementary cellular automaton starting with a single ON (black) cell. 1
1, 5, 8, 111, 64, 1919, 512, 31743, 4096, 516095, 32768, 8323071, 262144, 133693439, 2097152, 2143289343, 16777216, 34326183935, 134217728, 549487378431, 1073741824, 8793945538559, 8589934592, 140720308486143, 68719476736, 2251662374731775, 549755813888 (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 08 2016 and Apr 19 2019: (Start)

a(n) = 25*a(n-2)-152*a(n-4)+128*a(n-6) for n>5.

G.f.: (1+2*x)*(1+3*x-23*x^2+32*x^3-48*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).

(End)

MATHEMATICA

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]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)

CROSSREFS

Cf. A267001.

Sequence in context: A101016 A264295 A025518 * A151827 A258044 A162571

Adjacent sequences:  A267000 A267001 A267002 * A267004 A267005 A267006

KEYWORD

nonn

AUTHOR

Robert Price, Jan 08 2016

STATUS

approved

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Last modified December 15 17:03 EST 2019. Contains 330000 sequences. (Running on oeis4.)