A267160 Number of OFF (white) cells in the n-th iteration of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 2, 2, 3, 3, 6, 2, 11, 4, 13, 2, 19, 4, 21, 2, 27, 4, 29, 2, 35, 4, 37, 2, 43, 4, 45, 2, 51, 4, 53, 2, 59, 4, 61, 2, 67, 4, 69, 2, 75, 4, 77, 2, 83, 4, 85, 2, 91, 4, 93, 2, 99, 4, 101, 2, 107, 4, 109, 2, 115, 4, 117, 2, 123, 4, 125, 2, 131, 4, 133, 2

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 11 2016 and Apr 19 2019: (Start)

a(n) = a(n-2)+a(n-4)-a(n-6) for n>11.

G.f.: x*(2+2*x+x^3-x^4+x^5-x^6+4*x^7+x^8-x^9-x^10+x^11) / ((1-x)^2*(1+x)^2*(1+x^2)).

(End)

Mathematica

rule=107; 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. A267152.

Sequence in context: A035680 A238220 A103600 * A374436 A082861 A131704

Adjacent sequences: A267157 A267158 A267159 * A267161 A267162 A267163

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved