A267214 Total number of OFF (white) cells after n iterations of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 2, 7, 9, 13, 16, 26, 30, 37, 45, 57, 64, 76, 86, 101, 113, 127, 140, 160, 174, 191, 209, 231, 248, 270, 290, 315, 337, 361, 384, 414, 438, 465, 493, 525, 552, 584, 614, 649, 681, 715, 748, 788, 822, 859, 897, 939, 976, 1018, 1058, 1103, 1145, 1189

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-1)+a(n-3)-a(n-5)-a(n-7)+a(n-8) for n>7.

G.f.: x*(2+5*x^2+2*x^4-2*x^5+3*x^6) / ((1-x)^3*(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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)

Crossrefs

Cf. A243566.

Sequence in context: A011022 A070910 A189040 * A107386 A095021 A347913

Adjacent sequences: A267211 A267212 A267213 * A267215 A267216 A267217

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved