A267259 Number of ON (black) cells in the n-th iteration of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 3, 5, 5, 7, 6, 11, 6, 15, 6, 19, 6, 23, 6, 27, 6, 31, 6, 35, 6, 39, 6, 43, 6, 47, 6, 51, 6, 55, 6, 59, 6, 63, 6, 67, 6, 71, 6, 75, 6, 79, 6, 83, 6, 87, 6, 91, 6, 95, 6, 99, 6, 103, 6, 107, 6, 111, 6, 115, 6, 119, 6, 123, 6, 127, 6, 131, 6, 135, 6, 139

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) = (-2*(-1)^n*n+2*n+9*(-1)^n+3)/2 for n>4.

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

(End)

Mathematica

rule=111; 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[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

Crossrefs

Cf. A267253.

Sequence in context: A263721 A351259 A154290 * A002334 A115732 A246578

Adjacent sequences: A267256 A267257 A267258 * A267260 A267261 A267262

Keyword

nonn,easy

Author

Robert Price, Jan 12 2016

Status

approved