A267212 Total number of ON (black) cells after n iterations of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 7, 9, 16, 23, 33, 38, 51, 63, 76, 87, 105, 120, 139, 155, 176, 197, 221, 240, 267, 293, 320, 345, 377, 406, 439, 469, 504, 539, 577, 610, 651, 691, 732, 771, 817, 860, 907, 951, 1000, 1049, 1101, 1148, 1203, 1257, 1312, 1365, 1425, 1482, 1543, 1601

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

Crossrefs

Cf. A243566.

Sequence in context: A020894 A165995 A287575 * A022113 A041643 A041395

Adjacent sequences: A267209 A267210 A267211 * A267213 A267214 A267215

Keyword

nonn,easy

Author

Robert Price, Jan 11 2016

Status

approved