A267213 Number of OFF (white) cells in the n-th iteration of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 0, 5, 2, 4, 3, 10, 4, 7, 8, 12, 7, 12, 10, 15, 12, 14, 13, 20, 14, 17, 18, 22, 17, 22, 20, 25, 22, 24, 23, 30, 24, 27, 28, 32, 27, 32, 30, 35, 32, 34, 33, 40, 34, 37, 38, 42, 37, 42, 40, 45, 42, 44, 43, 50, 44, 47, 48, 52, 47, 52, 50, 55, 52, 54, 53

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 13 2016 and Apr 19 2019: (Start)

a(n) = a(n-3)+a(n-4)-a(n-7) for n>7.

G.f.: x*(2+5*x^2+2*x^4-2*x^5+3*x^6) / ((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2)).

(End)

Mathematica

rule=109; 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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)

Crossrefs

Cf. A243566.

Sequence in context: A359359 A066283 A240663 * A261805 A300703 A300706

Adjacent sequences: A267210 A267211 A267212 * A267214 A267215 A267216

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved