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A266979 Binary representation of the n-th iteration of the "Rule 79" elementary cellular automaton starting with a single ON (black) cell. 1
1, 110, 101, 1111010, 10101, 11111101010, 1010101, 111111110101010, 101010101, 1111111111010101010, 10101010101, 11111111111101010101010, 1010101010101, 111111111111110101010101010, 101010101010101, 1111111111111111010101010101010, 10101010101010101 (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 (0,10101,0,-1010100,0,1000000).

FORMULA

From Colin Barker, Jan 08 2016: (Start)

a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>5.

G.f.: (1+110*x-10000*x^2-100*x^3-100000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=79; 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+110*x-10000*x^2-100*x^3-100000*x^5)/((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)) + O(x^20)) \\ Colin Barker, Jan 08 2016

CROSSREFS

Cf. A266978.

Sequence in context: A278758 A281173 A281219 * A267138 A039724 A008944

Adjacent sequences:  A266976 A266977 A266978 * A266980 A266981 A266982

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 07 2016

STATUS

approved

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Last modified October 18 01:01 EDT 2018. Contains 316297 sequences. (Running on oeis4.)