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A266839 Decimal representation of the n-th iteration of the "Rule 67" elementary cellular automaton starting with a single ON (black) cell. 1
1, 4, 10, 97, 92, 1803, 736, 30815, 5888, 508671, 47104, 8263679, 376832, 133218303, 3014656, 2139488255, 24117248, 34295775231, 192937984, 549244108799, 1543503872, 8791999381503, 12348030976, 140704739229695, 98784247808, 2251537820680191, 790273982464 (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 05 2016 and Apr 18 2019: (Start)

a(n) = 25*a(n-2)-152*a(n-4)+128*a(n-6) for n>9.

G.f.: (1+4*x-15*x^2-3*x^3-6*x^4-14*x^5-172*x^6-28*x^7+192*x^8-64*x^9) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).

(End)

MATHEMATICA

rule=67; 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. A266837.

Sequence in context: A059919 A143047 A156329 * A203179 A125855 A261842

Adjacent sequences:  A266836 A266837 A266838 * A266840 A266841 A266842

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 04 2016

STATUS

approved

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Last modified June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)