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A267161 Total number of OFF (white) cells after n iterations of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell. 1
0, 2, 4, 6, 9, 12, 18, 20, 31, 35, 48, 50, 69, 73, 94, 96, 123, 127, 156, 158, 193, 197, 234, 236, 279, 283, 328, 330, 381, 385, 438, 440, 499, 503, 564, 566, 633, 637, 706, 708, 783, 787, 864, 866, 949, 953, 1038, 1040, 1131, 1135, 1228, 1230, 1329, 1333 (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 12 2016 and Apr 19 2019: (Start)

a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+a(n-7) for n>12.

G.f.: x*(2+2*x+x^3-x^4+x^5-x^6+4*x^7+x^8-x^9-x^10+x^11) / ((1-x)^3*(1+x)^2*(1+x^2)).

(End)

MATHEMATICA

rule=107; 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. A267152.

Sequence in context: A238374 A133041 A079492 * A173784 A094660 A005690

Adjacent sequences:  A267158 A267159 A267160 * A267162 A267163 A267164

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 11 2016

STATUS

approved

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Last modified January 26 10:40 EST 2020. Contains 331279 sequences. (Running on oeis4.)