A267530 Number of OFF (white) cells in the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36

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 17 2016 and Apr 20 2019: (Start)

a(n) = a(n-1)+a(n-2)-a(n-3) for n>4.

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

(End)

Mathematica

rule=141; 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. A267525.

Essentially the same as A008619.

Sequence in context: A203967 A365398 A365399 * A050292 A181627 A071521

Adjacent sequences: A267527 A267528 A267529 * A267531 A267532 A267533

Keyword

nonn,easy

Author

Robert Price, Jan 16 2016

Status

approved