A267211 Number of ON (black) cells in the n-th iteration of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.

1, 1, 5, 2, 7, 7, 10, 5, 13, 12, 13, 11, 18, 15, 19, 16, 21, 21, 24, 19, 27, 26, 27, 25, 32, 29, 33, 30, 35, 35, 38, 33, 41, 40, 41, 39, 46, 43, 47, 44, 49, 49, 52, 47, 55, 54, 55, 53, 60, 57, 61, 58, 63, 63, 66, 61, 69, 68, 69, 67, 74, 71, 75, 72, 77, 77

Offset

0,3

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: (Start)

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

G.f.: (1+x+5*x^2+x^3+5*x^4+x^5+3*x^6-3*x^7) / ((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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

Crossrefs

Cf. A243566.

Sequence in context: A195343 A074454 A256110 * A201423 A155790 A200646

Adjacent sequences: A267208 A267209 A267210 * A267212 A267213 A267214

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved