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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 15:29 EDT 2020. Contains 337383 sequences. (Running on oeis4.)