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A267887 Binary representation of the n-th iteration of the "Rule 237" elementary cellular automaton starting with a single ON (black) cell. 2
1, 10, 11111, 1111111, 111111111, 11111111111, 1111111111111, 111111111111111, 11111111111111111, 1111111111111111111, 111111111111111111111, 11111111111111111111111, 1111111111111111111111111, 111111111111111111111111111, 11111111111111111111111111111 (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

Index entries for linear recurrences with constant coefficients, signature (101,-100).

FORMULA

From Colin Barker, Jan 22 2016: (Start)

a(n) = 101*a(n-1)-100*a(n-2) for n>3.

G.f.: (1-91*x+10201*x^2-10100*x^3) / ((1-x)*(1-100*x)).

(End)

MATHEMATICA

rule=237; 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 *)

PROG

(PARI) Vec((1-91*x+10201*x^2-10100*x^3)/((1-x)*(1-100*x)) + O(x^20)) \\ Colin Barker, Jan 22 2016

CROSSREFS

Cf. A267870.

Sequence in context: A267850 A267206 A091253 * A151582 A318794 A229229

Adjacent sequences:  A267884 A267885 A267886 * A267888 A267889 A267890

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 21 2016

STATUS

approved

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)